{"id":27449,"date":"2022-04-01T14:51:24","date_gmt":"2022-04-01T09:21:24","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=27449"},"modified":"2022-04-07T10:58:24","modified_gmt":"2022-04-07T05:28:24","slug":"big-ideas-math-answers-grade-7-chapter-10","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-7-chapter-10\/","title":{"rendered":"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume"},"content":{"rendered":"<p>Surface Area and Volume is an important concept to learn and score good marks.<a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-7\/\"> Big Ideas Math Answers Grade 7<\/a> Chapter 10 Surface Area and Volume pdf is here. Follow the detailed explanation of BIM Grade 7 Chapter 10 Surface Area and Volume and maximize your score. Get the detailed and explanatory concept and preparatory material from the upcoming sections.<\/p>\n<p>There are various topics covered in surface area and volume. You can find a surface area and volume for a solid and an opaque object too. There are different objects for which you can find surface area and volume. If you want to imagine the 3-dimensional view of an object then surface area and volume play a major role.<\/p>\n<h2>Big Ideas Math Book 7th Grade Answer Key Chapter 10 Surface Area and Volume<\/h2>\n<p>You can get the guided notes for Surface Area and Volume Chapter 10 here. We help to provide you with the best resources that benefit you in understanding the topics in a better way by which you can improve your math skills. The topics in this Chapter include Surface Areas of Prisms, Cylinders, Pyramids, Volume of Prism, Pyramids, Cross Sections of Three-Dimensional Figures.<\/p>\n<p>We make sure that you understand these topics by the end of this Chapter. We provide examples and different practice sums that help you to solve the problems on your own. You can practice different sums by taking different examples. For any further doubts refer to this site and you can get clarity on your doubts with a clearcut understanding. You can get line-to-line clarity by referring to our site which helps you to improve your basic skills.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Surface_Area_and_Volume_STEAM_Video\/Performance_Task\">Surface Area and Volume STEAM Video\/Performance Task<\/a><\/li>\n<li><a href=\"#Surface_Area_and_Volume_Getting_Ready_for_Chapter_10\">Surface Area and Volume Getting Ready for Chapter 10<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 1 Surface Areas of Prisms<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.1_Surface_Areas_of_Prisms\">Lesson 10.1 Surface Areas of Prisms<\/a><\/li>\n<li><a href=\"#Surface_Areas_of_Prisms_Homework_&amp;_Practice_10.1\">Surface Areas of Prisms Homework &amp; Practice 10.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Surface Areas of Cylinders<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.2_Surface_Areas_of_Cylinders\">Lesson 10.2 Surface Areas of Cylinders<\/a><\/li>\n<li><a href=\"#Surface_Areas_of_Cylinders_Homework_&amp;_Practice_10.2\">Surface Areas of Cylinders Homework &amp; Practice 10.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Surface Areas of Pyramids<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.3_Surface_Areas_of_Pyramids\">Lesson 10.3 Surface Areas of Pyramids<\/a><\/li>\n<li><a href=\"#Surface_Areas_of_Pyramids_Homework_&amp;_Practice_10.3\">Surface Areas of Pyramids Homework &amp; Practice 10.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Volumes of Prisms<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.4_Volumes_of_Prisms\">Lesson 10.4 Volumes of Prisms<\/a><\/li>\n<li><a href=\"#Volumes_of_Prisms_Homework_&amp;_Practice_10.4\">Volumes of Prisms Homework &amp; Practice 10.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Volumes of Pyramids<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.5_Volumes_of_Pyramids\">Lesson 10.5 Volumes of Pyramids<\/a><\/li>\n<li><a href=\"#Volumes_of_Pyramids_Homework_&amp;_Practice_10.5\">Volumes of Pyramids Homework &amp; Practice 10.5<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 6 Cross-Sections of Three-Dimensional Figures<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.6_Cross_Sections_of_Three-Dimensional_Figures\">Lesson 10.6 Cross Sections of Three-Dimensional Figures<\/a><\/li>\n<li><a href=\"#Cross_Sections_of_Three-Dimensional_Figures_Homework_&amp;_Practice_10.6\">Cross Sections of Three-Dimensional Figures Homework &amp; Practice 10.6<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 10 &#8211; Surface Area and Volume<\/strong><\/p>\n<ul>\n<li><a href=\"#Surface_Area_and_Volume_Connecting_Concepts\">Surface Area and Volume Connecting Concepts<\/a><\/li>\n<li><a href=\"#Surface_Area_and_Volume_Chapter_Review\">Surface Area and Volume Chapter Review<\/a><\/li>\n<li><a href=\"#Surface_Area_and_Volume_Practice_Test\">Surface Area and Volume Practice Test<\/a><\/li>\n<li><a href=\"#Surface_Area_and_Volume_Cumulative_Practice\">Surface Area and Volume Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Surface_Area_and_Volume_STEAM_Video\/Performance_Task\"><\/a>Surface Area and Volume STEAM Video\/Performance Task<\/h3>\n<p><strong>STEAM Video<\/strong><\/p>\n<p>Paper Measurements<br \/>\nThe thickness of a single piece of paper cannot be precisely measured using a ruler. What other method can you use to measure the thickness of a piece of paper?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27451\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 1\" width=\"98\" height=\"302\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-1.png 98w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-1-97x300.png 97w\" sizes=\"(max-width: 98px) 100vw, 98px\" \/><br \/>\nWatch the STEAM Video \u201cPaper Measurements.\u201d Then answer the following questions.<br \/>\n1. A stack of 500 pieces of paper is 2 inches tall. How tall is a stack of 250 pieces? 100 pieces? 10 pieces? How thick is a single piece of paper?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27452\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 2\" width=\"274\" height=\"165\" \/><br \/>\n2. You have a circular notepad. How can you find the volume of one piece of paper in the notepad?<\/p>\n<p>Answer:<br \/>\n1. for 250 pieces = 46750 cubic inches<br \/>\n2. volume = 187 cubic inches<\/p>\n<p>Explanation:<br \/>\n1. for 250 pieces = l w x h<br \/>\n250 pieces = 250 x 17 x 11<br \/>\npieces = 46750<br \/>\n100 pieces = 100 x 17 x 11<br \/>\npieces = 18,700<br \/>\n10 pieces = 10 x 17 x 11<br \/>\npieces = 1870<br \/>\npiece = 1 x 17 x 11<br \/>\npiece = 187<br \/>\n2. volume = l x w x h<br \/>\nvolume = 8.5 x 11 x 2<br \/>\nvolume = 187<br \/>\n<strong>Performance Task<\/strong><\/p>\n<p>Volumes and Surface Areas of Small Objects<br \/>\nAfter completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given the dimensions of a shipping box and the number of bouncy balls that fit in the box.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27453\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 3\" width=\"524\" height=\"330\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-3.png 524w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-3-300x189.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><br \/>\nYou will be asked to use the box to estimate the volume of each bouncy ball. Why might it be helpful to use the volume of a container of objects to estimate the volume of one of the objects?<\/p>\n<p>Answer:<br \/>\nThe volume of the object =11,809.8 cubic centimeters<\/p>\n<p>Explanation:<br \/>\nThe volume of rectangular prism = l x w x h<br \/>\nwhere l = length, w = width, h = height<br \/>\nrectangular prism = 27 x 27 x 16.2<br \/>\nvolume = 11,809.8 cubic centimeters<\/p>\n<h3><a id=\"Surface_Area_and_Volume_Getting_Ready_for_Chapter_10\"><\/a>Surface Area and Volume Getting Ready for Chapter 10<\/h3>\n<p><strong>Chapter Exploration<\/strong><br \/>\nQuestion 1.<br \/>\nWork with a partner. Perform each step for each of the given dimensions.<br \/>\n\u2022 Use 24 one-inch cubes to form a rectangular prism that has the given dimensions.<br \/>\n\u2022 Make a sketch of the prism.<br \/>\n\u2022 Find the surface area of the prism.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27454\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-4.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 4\" width=\"518\" height=\"378\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-4.png 518w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-4-300x219.png 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><\/p>\n<p>Answer:<br \/>\na . 52 inches<br \/>\nb . 98 inches<br \/>\nc . 76 inches<br \/>\nd . 70 inches<br \/>\ne . 68 inches<br \/>\nf . 64 inches<br \/>\ng . 52\u00a0<span style=\"font-size: 16px; font-style: normal; font-weight: 400;\">\u00a0<\/span><span style=\"font-size: 16px; font-style: normal; font-weight: 400;\">inches<\/span><\/p>\n<p>prism :<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33623\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-1.png\" alt=\"\" width=\"223\" height=\"144\" \/><\/p>\n<p>The surface area of the square prism = 2lw + 2lh + 2wh<br \/>\nThe surface area of the rectangle prism = 2(lw + lh + wh)<\/p>\n<p>Explanation:<br \/>\na . The surface area of the Rectangular prism = 2(lw + lh +wh)<br \/>\nwhere l = 4 w = 3 h = 2<br \/>\nrectangular prism =2(4 x 3) +(2 x 3) +(4 x 2)<br \/>\nprism = 2(12) + (6) +(8)<br \/>\nsurface area =2( 26)<br \/>\nsurface area = 52<br \/>\nb . The surface area of the Rectangular prism = 2(lw + lh +wh)<br \/>\nwhere l = 1 w = 1 h = 24<br \/>\nrectangular prism =2(1 x 1) +(1 x 24) +(1 x 24)<br \/>\nprism = 2(1) + (24) +(24)<br \/>\nsurface area =2( 49)<br \/>\nsurface area = 98<br \/>\nc . The surface area of the Rectangular prism = 2(lw + lh +wh)<br \/>\nwhere l = 1 w = 2 h = 12<br \/>\nrectangular prism =2(1 x 2) +(2 x 12)+(1 x 12)<br \/>\nprism = 2(2) + (24) +(12)<br \/>\nsurface area =2( 38)<br \/>\nsurface area = 76<br \/>\nd. The surface area of the Rectangular prism = 2(lw + lh +wh)<br \/>\nwhere l = 1 w = 3 h = 8<br \/>\nrectangular prism =2(1 x 3) +(3 x 8)+(1 x 8)<br \/>\nprism = 2(3) + (24) +(8)<br \/>\nsurface area =2( 35)<br \/>\nsurface area = 70<br \/>\ne . The surface area of the Rectangular prism = 2(lw + lh +wh)<br \/>\nwhere l = 1 w = 4 h = 6<br \/>\nrectangular prism =2(1 x 4) +(4 x 6)+(1 x 6)<br \/>\nprism = 2(4) + (24) +(6)<br \/>\nsurface area =2( 34)<br \/>\nsurface area = 68<br \/>\nf .\u00a0The surface area of the Rectangular prism = 2(lw + lh +wh)<br \/>\nwhere l = 2 w = 2 h = 6<br \/>\nrectangular prism =2(2 x 2) +(2 x 6)+(1 x 6)<br \/>\nprism = 2(4) + (12) +(6)<br \/>\nsurface area =2( 32)<br \/>\nsurface area = 64<br \/>\ng . \u00a0The surface area of the Rectangular prism = 2(lw + lh +wh)<br \/>\nwhere l = 2 w = 4 h = 3<br \/>\nrectangular prism =2(2 x 4) +(4 x 3)+(2 x 3)<br \/>\nprism = 2(8) + (12) +(6)<br \/>\nsurface area =2( 26)<br \/>\nsurface area = 52<\/p>\n<p>Question 2.<br \/>\n<strong>REASONING<\/strong><br \/>\nWork with a partner. If two blocks of ice have the same volume, the block with the greater surface area will melt faster. The blocks below have equal volumes. Which block will melt faster? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27455\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-5.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 5\" width=\"407\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-5.png 407w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-5-300x92.png 300w\" sizes=\"(max-width: 407px) 100vw, 407px\" \/><\/p>\n<p>Answer:<br \/>\nThe first block will melt faster.<\/p>\n<p>Explanation:<br \/>\nThe surface area of the square prism = 2lw + 2lh + 2wh<br \/>\nwhere l = 1ft w = 1ft h = 1 ft<br \/>\nsurface area = 2(1 x 1)+2(1 x 1) + 2(1 x 1)<br \/>\nsurface area = 2(1)+2(1) + 2(1)<br \/>\nsurface area = 2+2+2<br \/>\nsurface area = 6<br \/>\nThe surface area of the Rectangular prism = 2(lw + lh +wh)<br \/>\nwhere l = 2 w = 1 h = 0.5<br \/>\nrectangular prism =2(2 x 1) +(2 x 0.5) +(1 x 0.5)<br \/>\nprism = 2(2) + (1) +(0.5)<br \/>\nsurface area = 4 + 1 + 0.5<br \/>\nsurface area = 5.5<\/p>\n<p><strong>Vocabulary<\/strong><br \/>\nThe following vocabulary terms are defined in this chapter. Think about what each term might mean and record your thoughts.<br \/>\nlateral surface area<br \/>\nthe slant height of a pyramid<br \/>\nregular pyramid<br \/>\ncross-section<\/p>\n<p>Answer:<br \/>\nLateral Surface Area = The lateral surface of an object is all of the sides of the object, excluding its base and top.<br \/>\nSlant Height of a Pyramid = The slant height of an object is the distance measured along a lateral face from the base to the apex along the center of the face.<br \/>\nRegular Pyramid =\u00a0 In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle.<br \/>\nCross Section = a surface or shape exposed by making a straight cut through something, especially at the right angles to an axis. ( The cross-section of an octahedron is a square.)<\/p>\n<h3><a id=\"Lesson_10.1_Surface_Areas_of_Prisms\"><\/a>Lesson 10.1 Surface Areas of Prisms<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Writing a Formula for Surface Area<br \/>\nWork with a partner.<br \/>\na. Use the diagrams to write a formula for the surface area of a rectangular prism. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27456\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 1\" width=\"611\" height=\"165\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-1.png 611w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-1-300x81.png 300w\" sizes=\"(max-width: 611px) 100vw, 611px\" \/><br \/>\nb. Choose dimensions for a rectangular prism. Then draw the prism and use your formula in part(a) to find the surface area.<\/p>\n<p>Answer:<br \/>\na :<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33624\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-2.png\" alt=\"\" width=\"293\" height=\"171\" \/><\/p>\n<p>b : The surface area of the rectangular prism = 2(lw + lh + wh)<br \/>\nwhere l = length , w= width , h = height.<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Surface Areas of Prisms<br \/>\nWork with a partner.<br \/>\na. Identify the solid represented by the net. Then find the surface area of the solid.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27457\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 2\" width=\"323\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-2.png 323w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-2-300x185.png 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><br \/>\nb. Describe a method for finding the surface area of any prism.<\/p>\n<p>Answer:<br \/>\na : The surface area of the solid = 94<br \/>\nb :\u00a0 The surface area of the solid = 2(lw + lh + wh)<\/p>\n<p>Explanation:<br \/>\na :<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33624\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-2.png\" alt=\"\" width=\"293\" height=\"171\" \/><br \/>\nb :<br \/>\nThe surface area of the rectangular prism = 2(lw + lh + wh)<br \/>\nwhere l = length , w= width , h = height.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-27458\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 3\" width=\"185\" height=\"79\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the surface area of the prism.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27459\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-4.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 4\" width=\"130\" height=\"135\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the prism = 52 ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the prism = 2lw + 2lh + 2wh<br \/>\nsurface area = 2(2 x 3) + 2(3 x 4) +2(2&#215;4)<br \/>\nsurface area = 2(6) + 2(12) + 2(8)<br \/>\nsurface area = 12 + 24 + 16<br \/>\nsurface area = 52 ft<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27460\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-5.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 5\" width=\"176\" height=\"125\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the prism = 288 sq. m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the prism = 2lw + 2lh + 2wh<br \/>\nsurface area = 2(5 x 8) + 2(8 x 8) +2(5&#215;8) where l = 8m,w = 8m, h= 8m<br \/>\nsurface area = 2(40) + 2(64) + 2(40)<br \/>\nsurface area = 80 + 128 + 80<br \/>\nsurface area = 288 sq. m<\/p>\n<p>Question 3.<br \/>\nFind the surface area of the prism at the left.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27461\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-6.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 6\" width=\"156\" height=\"82\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the prism at the left\u00a0 = 288 sq. m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the prism = 2lw + 2lh + 2wh<br \/>\nsurface area = 2(5 x 12) + 2(12 x 13) +2(5&#215;13) where l = 13m,w = 5m, h= 12m<br \/>\nsurface area = 2(60) + 2(156) + 2(65)<br \/>\nsurface area = 120 + 312 + 130<br \/>\nsurface area = 562 sq. m<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 4.<\/p>\n<p><strong>WRITING<\/strong><br \/>\nExplain the meaning of each term in the formula for the surface area of a rectangular prism.<\/p>\n<p>Answer:<br \/>\nThe surface area of the rectangular prism = 2(lw + lh + wh)<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = 2(lw + lh + wh)<br \/>\nwhere l = length , w= width , h = height<\/p>\n<p>Question 5.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27462\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 7\" width=\"598\" height=\"120\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-7.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-7-300x60.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the triangular prism = 26 sq. cm<br \/>\nThe surface area of the bases of the prism = 26 sq. cm<\/p>\n<p>Explanation:<\/p>\n<p>The surface area of the triangular prism = 2B + ph<br \/>\nwhere B = area of the base, p = perimeter of the base, h = height<br \/>\nsurface area = 2( 3) + 4 (5)<br \/>\nsurface area = 6 + 20<br \/>\nsurface area = 26 sq. cm<br \/>\nThe surface area of the bases of the prism = ph + 2B<br \/>\nsurface area = 4(5) + 2(3)<br \/>\nsurface area = 26 sq. cm<br \/>\nThe area of the net of the prism = The sum of the areas of the bases and the lateral faces of the prism.<\/p>\n<p>Question 6.<br \/>\nYou want to stain the lateral faces of the wooden chest shown. Find the area that you want to stain in square inches.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27463\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-8.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 8\" width=\"120\" height=\"105\" \/><\/p>\n<p>Answer:<br \/>\nThe area that you want to stain in square inches = 3456 square inches.<\/p>\n<p>Explanation:<br \/>\nThe surface area of the lateral faces of the prism = ph + 2B<br \/>\nsurface area = 4(4) + 2(4)<br \/>\nsurface area = 24 ft<br \/>\n1 feet = 144 square inches<br \/>\n144 x 24 = 3456 square inches.<\/p>\n<p>Question 7.<br \/>\nOne can of frosting covers about 280 square inches. Is one can of frosting enough to frost the cake? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27464\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-9.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 9\" width=\"293\" height=\"138\" \/><br \/>\nAnswer:<br \/>\nno one can of frosting is not enough to frost the cake.<\/p>\n<p>Explanation:<br \/>\nThe cake piece is in the shape of a rectangle<br \/>\nThe surface area of the rectangular prism = 2(lw + lh + wh)<br \/>\nwhere l = length , w= width , h = height<br \/>\nsurface area = 2(39 + 117 + 27)<br \/>\n183 sq. inches.<\/p>\n<p>Question 8.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nFind the surface area of the bench shown. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27465\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-10.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 10\" width=\"220\" height=\"134\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the bench = 16 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = 2(lw + lh + wh)<br \/>\nwhere l = length , w= width , h = height<br \/>\nsurface area = 2(1 x 1.5) +(1.5 x 2) +(2 x 5)<br \/>\nsurace area = 2(1.5) + 3 + 10<br \/>\nsurface area = 16 sq. ft<\/p>\n<h3><a id=\"Surface_Areas_of_Prisms_Homework_&amp;_Practice_10.1\"><\/a>Surface Areas of Prisms Homework &amp; Practice 10.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><br \/>\n<strong>Classify the pair of angles. Then find the value of x.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27466\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 11\" width=\"146\" height=\"91\" \/><\/p>\n<p>Answer:<br \/>\nThe value of x = 146<\/p>\n<p>Explanation:<br \/>\nThe above-shown angle = obtuse angle<br \/>\ngiven that 34 degrees<br \/>\n180 &#8211; 34 = 146<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27467\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-12.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 12\" width=\"108\" height=\"105\" \/><br \/>\nAnswer:<br \/>\nThe value of x = 106<\/p>\n<p>Explanation:<br \/>\nThe above-shown angle = right angle<br \/>\ngiven that 74 degrees<br \/>\n180 &#8211; 74 = 106Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27468\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-13.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 13\" width=\"148\" height=\"108\" \/><br \/>\nAnswer:<br \/>\nThe value of x = 121<\/p>\n<p>Explanation:<br \/>\nThe above-shown angle = acute angles.<br \/>\ngiven that 59 degrees<br \/>\nx + 10 = 59<br \/>\nx = 49<br \/>\n180 &#8211; 49 = 121<\/p>\n<p>Question 3.<\/p>\n<p><strong>Find the area of a circle with the indicated dimensions. Use 3.14 or \\(\\frac{22}{7}\\) for \u03c0.<\/strong><br \/>\nQuestion 4.<br \/>\nradius: 21 in.<\/p>\n<p>Answer:<br \/>\nThe area of the circle = 1,384.74 sq. in<\/p>\n<p>Explanation:<br \/>\nThe area of the circle = \u03c0r<sup>2<\/sup><br \/>\narea = 3.14 x 21 x 21 where \u03c0 = 3.14 radius = 21 in<br \/>\narea = 1,384.74 sq. in<br \/>\nQuestion 5.<br \/>\ndiameter: 36mm<br \/>\nAnswer:<br \/>\nThe area of the circle = 530.66 sq. mm<\/p>\n<p>Explanation:<br \/>\nThe area of the circle = \u03c0r<sup>2<\/sup><br \/>\narea = 3.14 x 13 x 13 where \u03c0 = 3.14 radius = 13 mm<br \/>\narea = 530.66 sq. mm<\/p>\n<p>Question 6.<br \/>\nradius: 8.5 m<\/p>\n<p>Answer:<br \/>\nThe area of the circle = 226.865 sq. m<\/p>\n<p>Explanation:<br \/>\nThe area of the circle = \u03c0r<sup>2<\/sup><br \/>\narea = 3.14 x 8.5 x 8.5 where \u03c0 = 3.14 radius = 8.5 m<br \/>\narea = 226.865 sq. m<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>SURFACE AREA OF A PRISM<\/strong> Identify the solid represented by the net. Then find the surface area of the solid. (See Explorations 1 &amp; 2, p. 409.)<br \/>\nQuestion 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27469\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-14.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 14\" width=\"236\" height=\"173\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the prism = 182<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = 2(lw + lh + wh)<br \/>\nwhere l = length , w= width , h = height<br \/>\nsurface area = 2(6 x 8) +(9 x 6) +(10 x 8)<br \/>\nsurace area = 2(48) + 54 + 80<br \/>\nsurface area = 182<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27470\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-15.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 15\" width=\"195\" height=\"173\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the prism = 44<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = 2(lw + lh + wh)<br \/>\nwhere l = length , w= width , h = height<br \/>\nsurface area = 2(5 x 2) +(2 x 3) +(3 x 2)<br \/>\nsurace area = 2(10) + 6+ 6<br \/>\nsurface area = 44 sq. units<\/p>\n<p><strong>FINDING THE SURFACE AREA OF A PRISM<\/strong> Find the surface area of the prism.<br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27471\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-16.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 16\" width=\"156\" height=\"107\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the prism = 324 sq. m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = 2(lw + lh + wh)<br \/>\nwhere l = length , w= width , h = height<br \/>\nsurface area = 2(6 x 16) +(16 x 3) +(3 x 6)<br \/>\nsurace area = 2(96) + 48+ 18<br \/>\nsurface area = 324 sq. m<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27472\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-17.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 17\" width=\"123\" height=\"114\" \/><\/p>\n<p>Answer:<br \/>\nThe surface area of the prism = 294 sq. yd<\/p>\n<p>Explanation:<br \/>\nThe surface area of the prism = 2lw + 2lh + 2wh<br \/>\nsurface area = 2(7 x 7)+ 2(7 x 7) +2(7&#215;7)<br \/>\nsurface area = 2(49) + 2(49) + 2(49)<br \/>\nsurface area = 98 + 98 + 98<br \/>\nsurface area = 294 sq. yd<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27473\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-18.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 18\" width=\"154\" height=\"102\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the triangular prism = 32 sq. m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular prism = 2B + ph<br \/>\nwhere B = area of the base, p = perimeter of the base, h = height<br \/>\nsurface area = 2( 6) + 4 (5)<br \/>\nsurface area = 12 + 20<br \/>\nsurface area = 32 sq. m<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27474\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-19.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 19\" width=\"167\" height=\"121\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the triangular prism = 166 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular prism = 2B + ph<br \/>\nwhere B = area of the base, p = perimeter of the base, h = height<br \/>\nsurface area = 2( 15) + 17 (8)<br \/>\nsurface area = 30 + 136<br \/>\nsurface area = 166 sq. ft<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27475\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-20.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 20\" width=\"122\" height=\"154\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the prism = 46.4 yds<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = 2(lw + lh + wh)<br \/>\nwhere l = length , w= width , h = height<br \/>\nsurface area = 2(1.2 x 5) +(5 x 3) +(1.2 x 6)<br \/>\nsurace area = 2(1) + 15+ 7.2<br \/>\nsurface area = 23.2 x 2<br \/>\nsurface area = 46.4 sq. yds<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27476\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-21.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 21\" width=\"148\" height=\"124\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the prism = 693 sq. in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the paralleloram prism = 2(lw + lh + wh)<br \/>\nwhere l = length , w= width , h = height<br \/>\nsurface area = 2(9 x 10) +(9 x 13.5) +(13.5 x 10)<br \/>\nsurace area = 2(90) +121.5 + 135<br \/>\nsurface area = 346.5 x 2<br \/>\nsurface area = 693 sq. inches<\/p>\n<p>Question 15.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds the surface area of the prism. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27477\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-22.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 22\" width=\"453\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-22.png 453w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-22-300x71.png 300w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><br \/>\nAnswer:<br \/>\nyes my friend is correct.<\/p>\n<p>Explanation:<br \/>\nThe surface area of the prism = 2lw + 2lh + 2wh<br \/>\nsurface area = 2(5 x 3)+ 2(3 x 4) +2(5&#215;3)<br \/>\nsurface area = 2(15) + 2(12) + 2(15)<br \/>\nsurface area = 30+ 24 + 30<br \/>\nsurface area = 84 sq. cm<\/p>\n<p>Question 16.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA cube-shaped satellite has side lengths of 10 centimeters. What is the least amount of aluminum needed to cover the satellite?<br \/>\nAnswer:<br \/>\nThe least amount of aluminum needed to cover the satellite = 90 centimeters.<\/p>\n<p>Explanation:<br \/>\nGiven that cube has the side lengths of 10 and 10 centimeters<br \/>\n10 x 10 = 100<br \/>\n100 -10 = 90<br \/>\nso the least amount of aluminum needed to cover = 90 centimeters.<\/p>\n<p><strong>FINDING SURFACE AREA<\/strong> Find the surface area of the prism.<br \/>\nQuestion 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27478\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-23.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 23\" width=\"159\" height=\"82\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the triangular prism = 80 in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular prism = 2B + ph<br \/>\nwhere B = area of the base, p = perimeter of the base, h = height<br \/>\nsurface area = 2( 16) + 4 (12)<br \/>\nsurface area = 32 + 48<br \/>\nsurface area = 80 sq. in<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27479\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-24.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 24\" width=\"212\" height=\"90\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the prism = 58 sq. m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = 2(lw + lh + wh)<br \/>\nwhere l = length , w= width , h = height<br \/>\nsurface area = 2(4 x 4) +(4 x 2) +(2.5 x 2)<br \/>\nsurace area = 2(16) + 8+ 5<br \/>\nsurface area = 29 x 2<br \/>\nsurface area = 58 sq. m<\/p>\n<p>Question 19.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nDraw and label a rectangular prism that has a surface area of 158 square yards.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-33760\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-3-300x139.png\" alt=\"\" width=\"300\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-3-300x139.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-3.png 327w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = 2(lw + lh + wh)<br \/>\nwhere l = length , w= width , h = height<br \/>\nsurface area = 2(4 x 5) +(5x 6) +(4 x 7)<br \/>\nsurace area = 2(20) + 30+ 29<br \/>\nsurface area = 79 x 2<br \/>\nsurface area = 158 square yards<\/p>\n<p>Question 20.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA label that wraps around a box of golf balls covers 75% of its lateral surface area. What is the value of x?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27480\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-25.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 25\" width=\"186\" height=\"141\" \/><br \/>\nAnswer:<br \/>\nThe value of x = 25%<\/p>\n<p>Explanation:<br \/>\nGiven that the label that wraps around a box of golf covers 75%<br \/>\nThat means for 100%<br \/>\n100 &#8211; 75 = 25%<\/p>\n<p>Question 21.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nYou are painting the prize pedestals shown(including the bottoms). You need 0.5 pint of paint to paint the red pedestal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27481\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-26.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 26\" width=\"325\" height=\"175\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-26.png 325w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-26-300x162.png 300w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><br \/>\na. The edge lengths of the green pedestal are one-half the edge lengths of the red pedestal. How much paint do you t do you need to paint the green pedestal?<br \/>\nb. The edge lengths of the blue pedestal are triple the edge lengths of the green pedestal. How much paint do you need to paint the blue pedestal?<br \/>\nc. Compare the ratio of paint volumes to the ratio of edge lengths for the green and red pedestals. Repeat for the green and blue pedestals. What do you notice?<br \/>\nAnswer:<br \/>\na. The paint you need to paint the green pedestal =1024 in<br \/>\nb. The paint you need to paint the blue pedestal = 5798464 in<br \/>\nc. 1 : 2 for green and red , 1 : 3 for green and blue.<br \/>\nb. Explanation:<br \/>\nThe surface area of the rectangular prism = 2(lw + lh + wh)<br \/>\nwhere l = length , w= width , h = height<br \/>\nsurface area = 2(16 x 16) +(16x 24) +(16 x 24)<br \/>\nsurace area = 2(256) + 384+ 384<br \/>\nsurface area = 1024 x 2<br \/>\nsurface area = 2048 sq. in<\/p>\n<p>Question 22.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nA key chain-sized puzzle cube is made up of small cubes. Each small cube has a surface area of 1.5 square inches.<br \/>\na. What is the edge length of each small cube?<br \/>\nb. What is the surface area of the entire puzzle cube?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27482\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.1-27.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.1 27\" width=\"150\" height=\"119\" \/><br \/>\nAnswer:<br \/>\nThe edge length of each small cube = 1<br \/>\nThe surface area of the entire puzzle cube\u00a0 = 81<\/p>\n<p>Explanation:<br \/>\nThe surface area of the prism = 2lw + 2lh + 2wh<br \/>\nsurface area = 2(0 x 0)+ 2(0 x 0) +1.5(1x 1)<br \/>\nsurface area = 2(0) +2(0) +1.5(1)<br \/>\nsurface area = 0 + 0 + 1.5<br \/>\nsurface area = 1.5<br \/>\nThe surface area of the each small cube = 81<\/p>\n<h3><a id=\"Lesson_10.2_Surface_Areas_of_Cylinders\"><\/a>Lesson 10.2 Surface Areas of Cylinders<\/h3>\n<p>A is a solid that has two parallel, identical circular bases.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27483\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-1.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 1\" width=\"219\" height=\"130\" \/><\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Finding the Surface Area of a Cylinder<br \/>\nWork with a partner.<br \/>\na. Make a net for the can. Name each shape in the net.<br \/>\nb. How are the dimensions of the paper related to the dimensions of the can?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27484\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-2.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 2\" width=\"201\" height=\"241\" \/><br \/>\nc. Write a formula that represents the surface area of a cylinder with h a height of and bases with a radius of r.<br \/>\nd. Estimate the dimensions of each can. Then use your formula in part(c) to estimate the surface area of each can.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27485\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-3.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 3\" width=\"549\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-3.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-3-300x93.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><br \/>\nAnswer:<br \/>\na. <img loading=\"lazy\" class=\"alignnone size-medium wp-image-33765\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-4-300x195.png\" alt=\"\" width=\"300\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-4-300x195.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-4.png 378w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nb. The dimensions of the paper = the dimensions of the can<br \/>\nc .<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-33765\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-4-300x195.png\" alt=\"\" width=\"300\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-4-300x195.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-4.png 378w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nd. The surface area of the cylinder = 2\u03c0r (h + r)<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the surface area of the cylinder. Round your answer to the nearest tenth if necessary.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27486\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-4.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 4\" width=\"148\" height=\"143\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the cylinder = 34138.08 sq. yd<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere r = radius, h = height<br \/>\n2 x 3.14 x 36 + 2 x 3.14 x 6 x 9<br \/>\n226.08 + 33912<br \/>\n34138.08<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27487\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-5.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 5\" width=\"223\" height=\"106\" \/><br \/>\nAnswer:<\/p>\n<p>The surface area of the cylinder = 395.64 sq. cm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere r = radius, h = height<br \/>\n2 x 3.14 x 9+ 2 x 3.14 x 3 x 18<br \/>\n56.52 + 339.12<br \/>\n395.64 sq. cms<\/p>\n<p><strong>Find the lateral surface area of the cylinder. Round your answer to the nearest tenth.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27488\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-6.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 6\" width=\"161\" height=\"130\" \/><br \/>\nAnswer:<br \/>\nThe lateral surface of the cylinder = 75.36 sq. cms<\/p>\n<p>Explanation:<br \/>\nThe lateral surface area of the cylinder = 2\u03c0rh<br \/>\narea = 2 x 3.14 x 3 x 4<br \/>\narea = 75.36 sq. cms<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27489\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-7.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 7\" width=\"100\" height=\"177\" \/><br \/>\nAnswer:<br \/>\nThe lateral surface of the cylinder = 150.72 sq. yds<\/p>\n<p>Explanation:<br \/>\nThe lateral surface area of the cylinder = 2\u03c0rh<br \/>\narea = 2 x 3.14 x 3 x 8<br \/>\narea = 150.72 sq. yds<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 5.<br \/>\nWRITING<br \/>\nWhich part of the formula S = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh represents the lateral surface area of a cylinder? the areas of the bases?<br \/>\nAnswer:<br \/>\nThe area of the bases of the cylinder.<\/p>\n<p>Explanation:<br \/>\nThe area of the bases of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere r = radius , h = height<\/p>\n<p>Question 6.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nYou are given the height of a cylinder and the circumference of its base. Describe how to find the surface area of the cylinder.<br \/>\nAnswer:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<\/p>\n<p>Explanation:<br \/>\nThe area of the bases of the cylinder =2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere r = radius, h = height<\/p>\n<p>Question 7.<br \/>\n<strong>FINDING A SURFACE AREA<\/strong><br \/>\nFind the surface area of the cylinder at the left. Round your answer to the nearest tenth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27490\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-8.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 8\" width=\"193\" height=\"94\" \/><br \/>\nAnswer:<br \/>\nThe lateral surface of the cylinder = 351.68 sq. in<\/p>\n<p>Explanation:<br \/>\nThe lateral surface area of the cylinder = 2\u03c0rh<br \/>\narea = 2 x 3.14 x 16 + 2 x 3.14x 4 x 10<br \/>\narea = 100.48 + 251.2<br \/>\narea = 351.68 sq. in<\/p>\n<p>Question 8.<br \/>\n<strong>FINDING A LATERAL SURFACE AREA<\/strong><br \/>\nFind the lateral surface area of the cylinder at the right. Round your answer to the nearest tenth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27491\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-9.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 9\" width=\"130\" height=\"87\" \/><br \/>\nAnswer:<\/p>\n<p>The lateral surface of the cylinder = 351 sq. in<\/p>\n<p>Explanation:<br \/>\nThe lateral surface area of the cylinder = 2\u03c0rh<br \/>\narea = 2 x 3.14 x 16 + 2 x 3.14x 4 x 10<br \/>\narea = 100.48 + 251.2<br \/>\narea = 351.68 sq. in<br \/>\nIN the question given that round to the nearest tenth<br \/>\narea = 351 sq. in<\/p>\n<p>Question 9.<br \/>\nYou remove the lid of the can. What is the percent of change in the surface area of the can?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27492\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-10.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 10\" width=\"174\" height=\"193\" \/><br \/>\nAnswer:<br \/>\nThe percent of the change in the surface area of the can = 22,019.25 mm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the can = 2\u03c0 rx r+ 2\u03c0rh<br \/>\n2 x 3.14 x 1806.25 + 2 x 3.14 x 42.5 x 40<br \/>\n22,019.25 mm<br \/>\nThe surface area of the triangular prism = 166 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular prism = 2B + ph<br \/>\nwhere B = area of the base, p = perimeter of the base, h = height<br \/>\nsurface area = 2( 15) + 17 (8)<br \/>\nsurface area = 30 + 136<br \/>\nsurface area = 166 sq. ft<\/p>\n<p>Question 10.<br \/>\nAfter burning half of a cylindrical candle, the surface area is 176 square inches. The radius of the candle is 2 inches. What was the original height of the candle?<br \/>\nAnswer:<br \/>\nThe original height of the<\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe area of the sheet of wrapping paper is equal to the lateral surface area of a cylindrical tube. The tube is 14 inches tall. What is the surface area of the tube, including the bases? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27493\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-11.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 11\" width=\"196\" height=\"111\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the tube including the bases = 42.96 inches<\/p>\n<p>Explanation:<br \/>\nThe lateral surface area of the cylinder = 2 x 3.14 x r x h<br \/>\nsurface area = 2 x 3.14 x 13 x 14<br \/>\nsurface area = 1142.96 inchs<\/p>\n<h3><a id=\"Surface_Areas_of_Cylinders_Homework_&amp;_Practice_10.2\"><\/a>Surface Areas of Cylinders Homework &amp; Practice 10.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the surface area of the prism.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27494\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-12.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 12\" width=\"139\" height=\"108\" \/><br \/>\nAnswer:<\/p>\n<p>The surface area of the prism = 142 sq. cms<\/p>\n<p>Explanation:<br \/>\nThe surface area of the prism = 2lw + 2lh + 2wh<br \/>\nsurface area = 2(7 x 3)+ 2(3 x 5) +2(5&#215;7)<br \/>\nsurface area = 2(21) + 2(15) + 2(35)<br \/>\nsurface area = 42+ 30 + 70<br \/>\nsurface area = 142 sq. cm<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27495\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-13.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 13\" width=\"162\" height=\"117\" \/><br \/>\nAnswer:<\/p>\n<p>The surface area of the triangular prism = 649 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular prism = 2B + ph<br \/>\nwhere B = area of the base, p = perimeter of the base, h = height<br \/>\nsurface area = 2( 20) + 29 (21)<br \/>\nsurface area = 40+ 609<br \/>\nsurface area = 649 sq. ft<\/p>\n<p>Question 3.<br \/>\nWhich of the following is equivalent to 0.625?<br \/>\nA. \\(\\frac{5}{8}\\)<br \/>\nB. \\(\\frac{625}{100}\\)<br \/>\nC. 0.625%<br \/>\nD. 6.25%<br \/>\nAnswer:<br \/>\nA is the correct answer<\/p>\n<p>Explanation:<br \/>\n(5\/8) = 0.625<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>FINDING SURFACE AREA<\/strong> Find the surface area of the cylinder. (See Exploration 1, p. 415.)<br \/>\nQuestion 4.<br \/>\na can with a radius of 60 millimeters and a height of 160 millimeters<br \/>\nAnswer:<br \/>\nThe surface area of the cylinder = 82,896 millimeters<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere\u00a0 radius = 60 millimeters , height = 160 given<br \/>\nsurface area = 2 x 3.14 x 60 x 60 + 2 x 3.14 x 60 x 160<br \/>\nsurface area = 22608 + 60,288<br \/>\nsurface area = 82,896 sq. millimeters<\/p>\n<p>Question 5.<br \/>\na hay bale with a diameter of 30 inches and a height of 72 inches<br \/>\nAnswer:<br \/>\nThe surface area of the cylinder = 8195.4 inches<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere\u00a0 radius = 15 inches , height = 72 inches given<br \/>\nsurface area = 2 x 3.14 x 15 x 15 + 2 x 3.14 x 15 x 72<br \/>\nsurface area = 1413 + 6,782.4<br \/>\nsurface area = 8195.4 sq. inches<\/p>\n<p><strong>FINDING SURFACE AREA<\/strong> Find the surface area of the cylinder. Round your answer to the nearest tenth if necessary.<br \/>\nQuestion 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27496\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-14.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 14\" width=\"153\" height=\"101\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the cylinder = 94.2 ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere\u00a0 radius = 3 ft , height = 2 ft given<br \/>\nsurface area = 2 x 3.14 x 3 x 3 + 2 x 3.14 x 3 x 2<br \/>\nsurface area = 56.52 + 37.68<br \/>\nsurface area = 94.2 sq. ft<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27497\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-15.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 15\" width=\"133\" height=\"85\" \/><br \/>\nAnswer:<\/p>\n<p>The surface area of the cylinder = 31.4 sq. m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere\u00a0 radius = 1 m , height = 4 m given<br \/>\nsurface area = 2 x 3.14 x 1 x 1 + 2 x 3.14 x 1 x 4<br \/>\nsurface area = 6.28+ 25.12<br \/>\nsurface area = 31.4 sq. m<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27498\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-16.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 16\" width=\"155\" height=\"104\" \/><br \/>\nAnswer:<\/p>\n<p>The surface area of the cylinder = 527.52 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere\u00a0 radius = 7 ft , height = 5 ft given<br \/>\nsurface area = 2 x 3.14 x 7 x 7 + 2 x 3.14 x 7 x 5<br \/>\nsurface area = 307.72+ 219.8<br \/>\nsurface area = 527.52 sq. ft<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27499\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-17.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 17\" width=\"172\" height=\"95\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the cylinder = 87.92 sq. mm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere\u00a0 radius = 2mm , height = 5 mm given<br \/>\nsurface area = 2 x 3.14 x 2 x 2 + 2 x 3.14 x 2 x 5<br \/>\nsurface area = 25.12+ 62.8<br \/>\nsurface area = 87.92 sq. mm<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27500\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-18.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 18\" width=\"117\" height=\"107\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the cylinder = 489.84 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere\u00a0 radius = 6 ft , height = 7 ft given<br \/>\nsurface area = 2 x 3.14 x 6 x 6 + 2 x 3.14 x 6 x 7<br \/>\nsurface area = 226.08+ 263.76<br \/>\nsurface area = 489.84 sq. ft<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27501\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-19.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 19\" width=\"187\" height=\"86\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the cylinder = 678.24 sq. cm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere\u00a0 radius = 6 cm , height = 12 cm given<br \/>\nsurface area = 2 x 3.14 x 6 x 6 + 2 x 3.14 x 6 x 12<br \/>\nsurface area = 226.08+ 452.16<br \/>\nsurface area = 678.24 sq. cm<\/p>\n<p><strong>FINDING LATERAL SURFACE AREA<\/strong> Find the lateral surface area of the cylinder. Round your answer to the nearest tenth if necessary.<br \/>\nQuestion 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27502\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-20.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 20\" width=\"145\" height=\"99\" \/><br \/>\nAnswer:<br \/>\nThe lateral surface area of the cylinder = 376.8 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder =\u00a0 2\u03c0rh<br \/>\nwhere\u00a0 radius = 10 ft , height = 6 ft given<br \/>\nsurface area =\u00a0 2 x 3.14 x 10 x 6<br \/>\nsurface area =\u00a0 376.8 sq. ft<br \/>\nQuestion 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27503\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-21.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 21\" width=\"155\" height=\"84\" \/><br \/>\nAnswer:<br \/>\nThe lateral\u00a0 surface area of the cylinder = 226.08 sq. in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder =\u00a0 2\u03c0rh<br \/>\nwhere\u00a0 radius = 4 in , height = 9 in given<br \/>\nsurface area =\u00a0 2 x 3.14 x 4 x 9<br \/>\nsurface area =\u00a0 226.08 sq. in<br \/>\nQuestion 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27504\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-22.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 22\" width=\"155\" height=\"89\" \/><br \/>\nAnswer:<br \/>\nThe lateral surface area of the cylinder = 87.92 sq. m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder =\u00a0 2\u03c0rh<br \/>\nwhere\u00a0 radius = 7 m , height = 2 m given<br \/>\nsurface area =\u00a0 2 x 3.14 x 7 x 2<br \/>\nsurface area =\u00a0 87.92 sq. m<br \/>\nQuestion 15.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds the surface area of the cylinder. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27505\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-23.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 23\" width=\"387\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-23.png 387w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-23-300x127.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><br \/>\nAnswer:<br \/>\nNo my friend is not correct.<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nsurface area = 2 x 3.14 x 5 x 5 + 2 x 3.14 x 5 x 10.6<br \/>\nsurface area = 157 + 332.84<br \/>\nsurface area = 489.84 sq. yds<\/p>\n<p>Question 16.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe tank of a tanker truck is a stainless steel cylinder. Find the surface area of the tank.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27506\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-24.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 24\" width=\"399\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-24.png 399w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-24-300x120.png 300w\" sizes=\"(max-width: 399px) 100vw, 399px\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the tank = 1356.48 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nsurface area = 2 x 3.14 x 4 x 4 + 2 x 3.14 x 4 x 50<br \/>\nsurface area = 100.48+ 1256<br \/>\nsurface area = 1,356.48 sq. ft<\/p>\n<p>Question 17.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe Petri dish shown has no lid. What is the surface area of the outside of the Petri dish?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27507\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-25.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 25\" width=\"182\" height=\"105\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the outside of the petri dish= 20,410 sq. mm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the outside of the petri dish = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nsurface area = 2 x 3.14 x 50 x 50 + 2 x 3.14 x 50x 15<br \/>\nsurface area = 15700+ 4710<br \/>\nsurface area = 20410 sq. mm<\/p>\n<p>Question 18.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou have two 8.5-by-11-inch pieces of paper. You form the lateral surfaces of two different cylinders by taping together a pair of opposite sides on each piece of paper so that one cylinder has a height of 8.5 inches and the other has a height of 11 inches. Without calculating, compare the surface areas of the cylinders (including the bases). Explain.<br \/>\nAnswer:<br \/>\nThe surface area of the cylinder 1= 44.826012 sq. inches<br \/>\nThe surface area of the cylinder 2= 56.915012 sq. inches<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder 1 = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nsurface area = 2 x 3.14 x 0.77 x 0.77 + 2 x 3.14 x 0.77x 8.5<br \/>\nsurface area = 3.723412+ 41.1026<br \/>\nsurface area = 44.826012 inches<br \/>\nThe surface area of the cylinder 1 = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nsurface area = 2 x 3.14 x 0.77 x 0.77 + 2 x 3.14 x 0.77x 11<br \/>\nsurface area = 3.723412+ 53.1916<br \/>\nsurface area = 56.915012 inches<\/p>\n<p>Question 19.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA ganza is a percussion instrument used in samba music.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27508\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-26.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 26\" width=\"230\" height=\"271\" \/><br \/>\na. Find the surface area of each of the two labeled ganzas.<br \/>\nb. The smaller ganza weighs 1.1 pounds. Assume that the surface area is proportional to the weight. What is the weight of the larger ganza?<br \/>\nAnswer:<br \/>\na. The surface area of the smaller ganza= 296.73 sq. cm<br \/>\nThe surface area of the larger ganza= 1036.2 sq. cm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the smaller ganza = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nsurface area = 2 x 3.14 x 3.5 x 3.5 + 2 x 3.14 x 3.5x 10<br \/>\nsurface area = 76.93+ 219.8<br \/>\nsurface area = 296.73 sq. cm<br \/>\nThe surface area of the larger ganza \u00a0= 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nsurface area = 2 x 3.14 x 5.5 x 5.5 + 2 x 3.14 x 5.5x 24.5<br \/>\nsurface area = 189.97+846.23<br \/>\nsurface area = 1036.2 sq. cm<\/p>\n<p>Question 20.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe wedge is one-eighth of the wheel of cheese.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27509\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-27.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 27\" width=\"216\" height=\"170\" \/><br \/>\na. Find the surface area of the cheese before it is cut.<br \/>\nb. Find the surface area of the remaining cheese after the wedge is removed. Did the surface area increase, decrease, or remain the same?<br \/>\nAnswer:<br \/>\na. The surface area of the cheese before it is cut= 75.36 sq. in<br \/>\nb. The surface area of the cheese after the wedge is removed = 58.875 sq. in<br \/>\nThe surface area decreases.<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cheese after the wedge is removed = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nsurface area = 2 x 3.14 x 3 x 3 + 2 x 3.14 x 3 x 1<br \/>\nsurface area = 56.52+ 18.84 in<br \/>\nsurface area = 75.36 sq. in<\/p>\n<p>The surface area of the cheese after the wedge is removed = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nsurface area = 2 x 3.14 x 3 x 3 + 2 x 3.14 x 3 x (1\/8) (1\/8) = 0.125<br \/>\nsurface area = 56.52+ 2.355<br \/>\nsurface area = 58.875 in<br \/>\nThe surface area decreases<\/p>\n<p>Question 21.<br \/>\n<strong>REPEATED REASONING<\/strong><br \/>\nA cylinder has radius r and height h.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27510\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.2-28.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.2 28\" width=\"105\" height=\"166\" \/><br \/>\na. How many times greater is the surface area of a cylinder when both dimensions are multiplied by2? 3? 5? 10?<br \/>\nb. Describe the pattern in part(a). Write an expression for the surface area of the cylinder when both dimensions are multiplied by a number.<br \/>\nAnswer:<br \/>\na. 2 times greater, 3 times greater, 5 times greater,10 times greater.<br \/>\nb. The expression for the surface area of the cylinder when both dimensions are multiplied 2 = 2r + 2h,3r + 3h,5r + 5h, 10r + 10 h<\/p>\n<h3><a id=\"Lesson_10.3_Surface_Areas_of_Pyramids\"><\/a>Lesson 10.3 Surface Areas of Pyramids<\/h3>\n<p>Many well-known pyramids have square bases, however, the base of a pyramid can be any polygon.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27511\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-1.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 1\" width=\"492\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-1.png 492w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-1-300x98.png 300w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Making a Scale Model<br \/>\nWork with a partner. Each pyramid below has a square base.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27512\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-2.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 2\" width=\"647\" height=\"219\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-2.png 647w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-2-300x102.png 300w\" sizes=\"(max-width: 647px) 100vw, 647px\" \/><br \/>\na. Draw a net for a scale model of one of the pyramids. Describe the scale factor.<br \/>\nb. Find the lateral surface area of the real-life pyramid that you chose in part(a). Explain how you found your answer.<br \/>\nc. Draw a net for a pyramid with a non-rectangular base and find its lateral surface area. Explain how you found your answer.<br \/>\nAnswer:<br \/>\na. <img loading=\"lazy\" class=\"alignnone size-full wp-image-33823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-5.png\" alt=\"\" width=\"186\" height=\"127\" \/><br \/>\nb. The lateral surface of the real life pyramid = A + (1\/2 ) ps<br \/>\nwhere A = area of base ,p= perimeter of base , s = slant height.<br \/>\nc. <img loading=\"lazy\" class=\"alignnone size-full wp-image-33824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-6.png\" alt=\"\" width=\"284\" height=\"213\" \/><br \/>\nThe lateral surface area of the rectangular pyramid = A + (1\/2)ps<br \/>\nwhere A = area of base ,p= perimeter of base , s = slant height.<br \/>\nA regular pyramid is a pyramid whose base is a regular polygon. The slant height lateral faces are triangles. The height of each triangle is the of the pyramid.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27513\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-3.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 3\" width=\"183\" height=\"110\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nWhat is the surface area of a square pyramid with a base side length of 9 centimeters and a slant height of 7 centimeters?<br \/>\nAnswer:<br \/>\nThe surface area of the square pyramid = 94.5 sq. centimeters<\/p>\n<p>Explanation:<br \/>\nThe surface area of the square pyramid = A + (1\/2) ps<br \/>\nwhere A = area of the base ,p = perimeter of th base, s = slant height<br \/>\nsurface area = 63 +(1\/2) 9 x 7<br \/>\nsurface area = 63 + 0.5 x\u00a0 63<br \/>\nsurface area = 31.5 + 63<br \/>\n94.5 sq. centimeters.<\/p>\n<p>Question 2.<br \/>\nFind the surface area of the regular pyramid at the left.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27514\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-4.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 4\" width=\"121\" height=\"162\" \/><br \/>\nAnswer:<\/p>\n<p>The surface area of the triangle pyramid = 86 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangle pyramid = A + (1\/2) ps<br \/>\nwhere A = area of the base ,p = perimeter of th base, s = slant height<br \/>\nsurface area = 60 +(1\/2) 5.2 x 10<br \/>\nsurface area = 60 + 2.6 x\u00a0 10<br \/>\nsurface area = 60+ 26<br \/>\nsurface area = 86 sq. ft<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 3.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nCan a pyramid have rectangles as lateral faces? Explain.<br \/>\nAnswer:<br \/>\nYes, pyramids have rectangles as lateral faces.<\/p>\n<p>Explanation:<br \/>\nIn the pyramid diagram, the rectangles included the lateral surfaces.<\/p>\n<p><strong>FINDING THE SURFACE AREA OF A PYRAMID<\/strong> Find the surface area of the regular pyramid.<br \/>\nQuestion 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27515\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-5.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 5\" width=\"157\" height=\"99\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the triangle pyramid = 95 sq. m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangle pyramid = A + (1\/2) ps<br \/>\nwhere A = area of the base ,p = perimeter of th base, s = slant height<br \/>\nsurface area = 65+(1\/2) 5 x 12<br \/>\nsurface area = 65 + 2.5 x\u00a0 12<br \/>\nsurface area = 65 + 30<br \/>\nsurface area = 95 sq. m<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27516\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-6.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 6\" width=\"85\" height=\"104\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the triangle pyramid = 24 sq. cm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangle pyramid = A + (1\/2) ps<br \/>\nwhere A = area of the base ,p = perimeter of th base, s = slant height<br \/>\nsurface area = 12+(1\/2) 2 x 6<br \/>\nsurface area = 12 + 1 x\u00a0 12<br \/>\nsurface area = 12 + 12<br \/>\nsurface area = 24 sq. cm<\/p>\n<p>Question 6.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich description of the solid does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27517\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-7.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 7\" width=\"495\" height=\"96\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-7.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-7-300x58.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><br \/>\nAnswer:<br \/>\nregular pyramid does not belong with the other three;<\/p>\n<p>Explanation:<br \/>\nthe remaining are square pyramid, rectangular pyramid, triangular pyramid are the three pyramids with different shapes.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 7.<br \/>\nA building in the shape of a square pyramid is covered with solar panels. The building has a slant height of 12 feet and a base with side lengths of 15 feet. The solar panels cost $70 per square foot to install. How much does it cost to install enough solar panels to cover the entire surface of the building?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27518\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-8.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 8\" width=\"167\" height=\"202\" \/><br \/>\nAnswer:<br \/>\n$ 270 is enough for solar planets to cover the entire surface of the building.<\/p>\n<p>Explanation:<br \/>\nThe building is in the shape of square pyramid.<br \/>\nsurface area = A + (1\/2) ps<br \/>\narea = 180 + (1\/2) x 180<br \/>\narea = 180 + 90<br \/>\narea = 270 $<\/p>\n<p>Question 8.<br \/>\nYou use the glass pyramid shown to display rainbows on the walls of a room. The pyramid is regular and has a surface area of 105.35 square centimeters. Find the height of each triangular face. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27519\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-9.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 9\" width=\"119\" height=\"125\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Surface_Areas_of_Pyramids_Homework_&amp;_Practice_10.3\"><\/a>Surface Areas of Pyramids Homework &amp; Practice 10.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the surface area of the cylinder. Round your answer to the nearest tenth.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27520\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-10.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 10\" width=\"145\" height=\"80\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the cylinder = 182.12 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere\u00a0 radius = 3 ft , height = 10 ft given<br \/>\nsurface area = 2 x 3.14 x 3 x 3 + 2 x 3.14 x 2 x 10<br \/>\nsurface area =\u00a0 56.52+ 125.6<br \/>\nsurface area = 182.12 sq. ft<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27522\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-11.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 11\" width=\"117\" height=\"109\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the cylinder = 345.4 sq. m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere\u00a0 radius = 5 m , height = 6 m given<br \/>\nsurface area = 2 x 3.14 x 5 x 5 + 2 x 3.14 x 5 x 6<br \/>\nsurface area =\u00a0 157+ 188.4<br \/>\nsurface area = 345.4 sq. m<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27523\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-12.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 12\" width=\"214\" height=\"108\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the cylinder = 406.944 sq. mm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere\u00a0 radius = 4mm , height = 12.2mm given<br \/>\nsurface area = 2 x 3.14 x 4 x 4+ 2 x 3.14 x 4 x 12.2<br \/>\nsurface area =\u00a0 100.48+ 306.464<br \/>\nsurface area = 406.944 sq. mm<\/p>\n<p>Question 4.<br \/>\nThe ratio of the distance between bases on a professional baseball field to the distance between bases on a youth baseball field is 3 : 2. Bases on a professional baseball field are 90 feet apart. What is the distance between bases on a youth baseball field?<br \/>\nA. 30 ft<br \/>\nB. 45 ft<br \/>\nC. 60 ft<br \/>\nD. 135 ft<br \/>\nAnswer:<br \/>\nThe distance between bases on a youth baseball = 60 ft<br \/>\nExplanation:<br \/>\nThe ratios between professional base and youth baseball = 3 : 2 already given<br \/>\n90 given<br \/>\nso 60 ft is the distance between bases on a youth baseball field.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>USING A NET<\/strong> Use the net to find the surface area of the regular pyramid. (See Exploration 1, p. 421.)<br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27524\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-13.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 13\" width=\"117\" height=\"107\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the square pyramid = 18 sq. in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the square pyramid = A + (1\/2) ps<br \/>\nwhere A = area of the base ,p = perimeter of th base, s = slant height<br \/>\nsurface area = 12+(1\/2) 4 x 3<br \/>\nsurface area = 12 + 0.5x\u00a0 12<br \/>\nsurface area = 12 + 6<br \/>\nsurface area = 18 sq. in<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27525\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-14.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 14\" width=\"151\" height=\"119\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the square pyramid = 88.3 sq. mm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the square pyramid = A + (1\/2) ps<br \/>\nwhere A = area of the base ,p = perimeter of th base, s = slant height<br \/>\nsurface area = 43.3+(1\/2) 10 x 9<br \/>\nsurface area = 43.3 + 0.5x\u00a0 90<br \/>\nsurface area = 43.3 + 45<br \/>\nsurface area = 88.3 sq. mm<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27526\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-15.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 15\" width=\"144\" height=\"110\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the square pyramid = 79.9 sq. m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the square pyramid = A + (1\/2) ps<br \/>\nwhere A = area of the base ,p = perimeter of the base, s = slant height<br \/>\nsurface area = 61.9 +(1\/2) 6 x 6<br \/>\nsurface area = 61.9 + 0.5x 36<br \/>\nsurface area = 61.9 + 18<br \/>\nsurface area = 79.9 sq. m<\/p>\n<p><strong>FINDING THE SURFACE AREA OF A PYRAMID<\/strong> Find the surface area of the regular pyramid.<br \/>\nQuestion 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27527\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-16.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 16\" width=\"107\" height=\"114\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the triangular\u00a0 pyramid = 81 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular pyramid = A + (1\/2) ps<br \/>\nwhere A = area of the base ,p = perimeter of the base, s = slant height<br \/>\nsurface area = 54 +(1\/2) 6 x 9<br \/>\nsurface area = 54 + 0.5x 54<br \/>\nsurface area = 54 + 27<br \/>\nsurface area = 81 sq. ft<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27528\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-17.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 17\" width=\"116\" height=\"109\" \/><br \/>\nAnswer:<\/p>\n<p>The surface area of the triangular\u00a0 pyramid = 36 sq. cm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular pyramid = A + (1\/2) ps<br \/>\nwhere A = area of the base ,p = perimeter of the base, s = slant height<br \/>\nsurface area = 24 +(1\/2) 6 x 4<br \/>\nsurface area = 24 + 0.5x 24<br \/>\nsurface area = 24 + 12<br \/>\nsurface area = 36 sq. cm<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27529\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-18.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 18\" width=\"148\" height=\"119\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the triangular\u00a0 pyramid = 36 sq. in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular pyramid = A + (1\/2) ps<br \/>\nwhere A = area of the base ,p = perimeter of the base, s = slant height<br \/>\nsurface area = 13\u00a0 +(1\/2) 15 x 10<br \/>\nsurface area = 13 + 0.5x 150<br \/>\nsurface area = 13 + 75<br \/>\nsurface area = 88 sq. in<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27530\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-19.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 19\" width=\"118\" height=\"136\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the triangular\u00a0 pyramid = 126 sq. yd<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular pyramid = A + (1\/2) ps<br \/>\nwhere A = area of the base ,p = perimeter of the base, s = slant height<br \/>\nsurface area = 7.8\u00a0 +(1\/2) 10 x 9<br \/>\nsurface area = 7.8 + 0.5x 90<br \/>\nsurface area = 7.8 + 48<br \/>\nsurface area = 126 sq. yd<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27531\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-20.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 20\" width=\"128\" height=\"114\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the triangular\u00a0 pyramid = 13.5 sq. m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular pyramid = A + (1\/2) ps<br \/>\nwhere A = area of the base ,p = perimeter of the base, s = slant height<br \/>\nsurface area = 4.5 +(1\/2) 4 x 4.5<br \/>\nsurface area = 4.5 + 0.5x 18<br \/>\nsurface area = 4.5 + 9<br \/>\nsurface area = 13.5 sq. m<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27532\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-21.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 21\" width=\"215\" height=\"134\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the triangular\u00a0 pyramid = 600.4 sq. mm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular pyramid = A + (1\/2) ps<br \/>\nwhere A = area of the base ,p = perimeter of the base, s = slant height<br \/>\nsurface area = 440.4 +(1\/2) 16 x 20<br \/>\nsurface area = 440.4+ 0.5x 320<br \/>\nsurface area = 440.4+ 160<br \/>\nsurface area = 600.4 sq. mm<\/p>\n<p>Question 14.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe base of the lampshade is a regular hexagon with side lengths of 8 inches. Estimate the amount of glass needed to make the lampshade.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27533\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-22.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 22\" width=\"180\" height=\"178\" \/><br \/>\nAnswer:<br \/>\nThe amount of glass needed to make the lampshade = 26.6666667 in<\/p>\n<p>Explanation:<br \/>\nhexagon = 1\/3 x b x h<br \/>\nwhere base = 8 inches , height = 10 in given<br \/>\nhexagon = (80\/3)<br \/>\nhexagon = 26.6666667 in<br \/>\nQuestion 15.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nThe surface area of a square pyramid is 85 square meters. The side length of the base is 5 meters. What is the slant height?<br \/>\nAnswer:<br \/>\nThe\u00a0 slant height = 6 meters<\/p>\n<p>Explanation:<br \/>\nThe area of the base = side x side = 5 x 5 = 25 m<br \/>\narea of the lateral face = (1\/2)bh= (1\/2)5h= 2.5 h m<br \/>\nThere are\u00a0 4 identical lateral faces.<br \/>\narea of lateral faces = 4(2.5h) = 10 hm<br \/>\nsurface area of regular pyramid = area of base + area of lateral faces<br \/>\n85 = 25 + 10 h<br \/>\n85-25 = 10 h<br \/>\n60 = 10 h<br \/>\nh = (60\/10)<br \/>\nh = 6 meters<\/p>\n<p><strong>FINDING SURFACE AREA<\/strong> Find the surface area of the solid.<br \/>\nQuestion 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27534\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-23.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 23\" width=\"135\" height=\"149\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the square\u00a0 pyramid = 20 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the square pyramid = A + (1\/2) ps<br \/>\nwhere A = area of the base ,p = perimeter of the base, s = slant height<br \/>\nsurface area = 5 +(1\/2) 5 x 6<br \/>\nsurface area = 5 + 0.5x 30<br \/>\nsurface area = 5\u00a0 + 15<br \/>\nsurface area = 20 sq. ft<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27535\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-24.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 24\" width=\"188\" height=\"144\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the square\u00a0 pyramid = 22 sq. cm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the square pyramid = A + (1\/2) ps<br \/>\nwhere A = area of the base ,p = perimeter of the base, s = slant height<br \/>\nsurface area = 10 +(1\/2) 4 x 6<br \/>\nsurface area = 10 + 0.5x 24<br \/>\nsurface area = 10 + 12<br \/>\nsurface area = 22 sq. cm<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27536\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-25.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 25\" width=\"216\" height=\"128\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the rectangular\u00a0 pyramid = 22 sq. ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular pyramid = A + (1\/2) ps<br \/>\nwhere A = area of the base ,p = perimeter of the base, s = slant height<br \/>\nsurface area = 12 +(1\/2) 4 x 5<br \/>\nsurface area = 12 + 0.5x 20<br \/>\nsurface area = 12 + 10<br \/>\nsurface area = 22 sq. ft<\/p>\n<p>Question 19.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nA tetrahedron is a triangular pyramid with four faces that are identical equilateral triangles. The total lateral surface area of a tetrahedron is 93 square centimeters. Find the surface area of the tetrahedron.<br \/>\nAnswer:<br \/>\nThe surface area\u00a0 of the tetrahedron = 124 square cm<\/p>\n<p>Explanation:<br \/>\nArea of lateral face (equilateral triangle) = 93\/3 = 31<br \/>\nThe tetrahedron has four identical equilateral triangles = 4 X 31 =124 cm<\/p>\n<p>Question 20.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou are making an umbrella that is shaped like a regular octagonal pyramid.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27537\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-26.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 26\" width=\"308\" height=\"133\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-26.png 308w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-26-300x130.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><br \/>\na. Estimate the amount of fabric that you need to make the umbrella.<br \/>\nb. The fabric comes in rolls that are 60 inches wide. Draw a diagram of how you can cut the fabric from rolls that are 10 feet long.<br \/>\nc. How much fabric is wasted?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33969\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-7.png\" alt=\"\" width=\"269\" height=\"281\" \/><\/p>\n<p>Question 21.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe height of a pyramid is the perpendicular distance between the base and the top of the pyramid. Which is greater, the height of a pyramid or the slant height? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27538\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-27.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 27\" width=\"182\" height=\"133\" \/><br \/>\nAnswer:<br \/>\nThe height of the pyramid is greater .<\/p>\n<p>Explanation:<br \/>\nIn the above shown figure the slant height is less than the height of the pyramid.<\/p>\n<p>Question 22.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nBoth pyramids at the right have regular bases.<br \/>\na. Without calculating, determine which pyramid has the greater surface area. Explain.<br \/>\nb. Verify your answer to part(a) by finding the surface area of each pyramid.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27539\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-10.3-28.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume 10.3 28\" width=\"230\" height=\"163\" \/><br \/>\nAnswer:<br \/>\nThe first figure has the greatest surface area.<\/p>\n<p>Explanation:<br \/>\nThe surface area of 1st pyramid = A + (1\/2) ps<br \/>\nsurface area = 112\u00a0 + (1\/2) 8 x 14<br \/>\nsurface area = 112 +(112\/2)<br \/>\nsurface area = 56 +112<br \/>\nsurface area = 168 in<br \/>\nThe surface area of 2nd pyramid = A + (1\/2) ps<br \/>\nsurface area = 6.9 + (1\/2) 8 x 14<br \/>\nsurface area = 6.9 +(112\/2)<br \/>\nsurface area = 56 +6.9<br \/>\nsurface area = 62.9 sq. in<\/p>\n<p>Question 23.<br \/>\n<strong>REASONING<\/strong><br \/>\nIs the total area of the lateral faces of a pyramid greater than, less than or equal to the area of the base? Explain.<br \/>\nAnswer:<br \/>\nThe lateral surface area of a regular pyramid is the sum of the area of its lateral faces.<br \/>\nThe total surface area of a regular pyramid is the sum of the areas of its lateral faces and its base.<\/p>\n<h3><a id=\"Lesson_10.4_Volumes_of_Prisms3\"><\/a>Lesson 10.4 Volumes of Prisms<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Finding a Formula for Volume<br \/>\nWork with a partner.<br \/>\na. In the figures shown, each cube has a volume of 1 cubic unit. Compare the volume V (in cubic units) of each rectangular prism to the area B(in square units) of its base. What do you notice?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27540\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 1\" width=\"414\" height=\"121\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-1.png 414w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-1-300x88.png 300w\" sizes=\"(max-width: 414px) 100vw, 414px\" \/><br \/>\nb. Repeat part(a) using the prisms below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27541\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-2.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 2\" width=\"393\" height=\"128\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-2.png 393w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-2-300x98.png 300w\" sizes=\"(max-width: 393px) 100vw, 393px\" \/><br \/>\nc. Use what you learned in parts (a) and (b) to write a formula that gives the volume of any prism.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27542\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-3.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 3\" width=\"588\" height=\"235\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-3.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-3-300x120.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><br \/>\nAnswer:<br \/>\na. The 1st cube has a volume of 1 cubic unit. and it is increased by one horizontal in each cube.<br \/>\nb. The 1st prism has a volume of 1 cubic unit and it is increased by one horizontal in each cube.<br \/>\nc. Triangular prism = 2B + ph<br \/>\nwhere b = base ,h = height, l = length, p = perimeter of base, B = area of base<br \/>\nRectangular prism = 2(lw +lh + wh)<br \/>\nwhere l = length, w = width, h = height<br \/>\npentagonal prism = (1\/2)(5s x a)h<br \/>\nHexagonal prism = v = bh<br \/>\noctagonal prism = 2(1 +square root )a square<\/p>\n<p>The volume of a three-dimensional figure is a measure of the amount of space that it occupies. Volume is measured in cubic units.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the volume of the prism.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27543\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-4.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 4\" width=\"121\" height=\"102\" \/><br \/>\nAnswer:<br \/>\nThe volume of the prism = 16 cu. ft<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = bh<br \/>\nwhere b = 4 ft , h = 4 ft given<br \/>\nvolume of the prism = 16 cu. ft<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27544\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-5.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 5\" width=\"164\" height=\"101\" \/><br \/>\nAnswer:<br \/>\nThe volume of the prism = 51 cu. cm<\/p>\n<p>Explanation:<br \/>\nThe volume of the prism = bh<br \/>\nwhere b = 8.5 cm , h = 6 cm given<br \/>\nvolume of the prism = 8.5 x 6 = 51 cu. cm<\/p>\n<p><strong>Find the volume of the prism.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27545\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-6.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 6\" width=\"150\" height=\"82\" \/><br \/>\nAnswer:<br \/>\nThe volume of prism = 162 cu. m<\/p>\n<p>Explanation:<br \/>\nThe volume of triangular prism = a x b x c x h<br \/>\nwhere a = b = c = base side , h = height<br \/>\nprism = 12 x 9 x 12 x 5<br \/>\nvolume = 60 + 102<br \/>\nvolume = 162 cu. m<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27546\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-7.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 7\" width=\"132\" height=\"156\" \/><br \/>\nAnswer:<\/p>\n<p>The volume of prism = 9 cu. m<\/p>\n<p>Explanation:<br \/>\nThe volume of triangular prism = a x b x c x h<br \/>\nwhere a = b = c = base side , h = height<br \/>\nprism = 0.75x 2 x 2 x 3<br \/>\nvolume = 0.75 x12<br \/>\nvolume = 9 cu. m<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>FINDING THE VOLUME OF A PRISM<\/strong> Find the volume of the prism.<br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27547\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-8.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 8\" width=\"154\" height=\"128\" \/><br \/>\nAnswer:<br \/>\nThe volume of the prism = 56 cu. in<\/p>\n<p>Explanation:<br \/>\nvolume v = B h<br \/>\nv = 7 x 8<br \/>\nv = 56 cu. in<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27548\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-9.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 9\" width=\"183\" height=\"93\" \/><br \/>\nAnswer:<br \/>\nThe volume of the prism = 75 cu. ft<\/p>\n<p>Explanation:<br \/>\nvolume v = B h<br \/>\nv = 15 x 5<br \/>\nv = 75 cu. ft<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27549\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-10.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 10\" width=\"152\" height=\"123\" \/><br \/>\nAnswer:<br \/>\nThe volume of the prism = 96 cu. yd<\/p>\n<p>Explanation:<br \/>\nvolume v = B h<br \/>\nv = 12 x 8<br \/>\nv = 96 cu. yd<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27550\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-11.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 11\" width=\"143\" height=\"129\" \/><br \/>\nAnswer:<br \/>\nThe volume of the prism = 4925 cu. mm<\/p>\n<p>Explanation:<br \/>\nvolume v = B h<br \/>\nv = 197 x 25<br \/>\nv = 4925 cu. mm<\/p>\n<p>Question 9.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nDraw and label a prism with a volume of 144 cubic inches. Justify your answer.<br \/>\nAnswer:<br \/>\nv = b x h<br \/>\n144 = 12 x 12<br \/>\nso base = 7 and height = 7 inches.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-33979\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-8-300x168.png\" alt=\"\" width=\"300\" height=\"168\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-8-300x168.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-8.png 308w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou visit an aquarium. One of the tanks at the aquarium holds 450 gallons of water. Draw a diagram to show one possible set of dimensions of the tank. Justify your answer. (1 gal = 231 in.<sup>3<\/sup>)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27551\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-12.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 12\" width=\"169\" height=\"193\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nA stack of paper contains 400 sheets. The volume of the stack is 140.25 cubic inches. Each sheet of paper is identical, with a length of 11 inches and a width of 8.5 inches. Find the height of each sheet of paper. Justify your answer.<br \/>\nAnswer:<br \/>\nEach sheet of paper = 0.0075 inches.<\/p>\n<h3><a id=\"Volumes_of_Prisms_Homework_&amp;_Practice_10.4\"><\/a>Volumes of Prisms Homework &amp; Practice 10.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the surface area of the regular pyramid.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27552\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-13.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 13\" width=\"100\" height=\"133\" \/><br \/>\nAnswer:<br \/>\nSurface area of the regular pyramid = 15 sq. m<\/p>\n<p>Explanation:<br \/>\nSurface area of the regular pyramid = A + (1\/2) ps<br \/>\narea = 3 +(1\/2) 3 x 8<br \/>\nsurface area = 3 + 12<br \/>\nsurface area = 15 sq. m<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27553\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-14.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 14\" width=\"159\" height=\"102\" \/><br \/>\nAnswer:<br \/>\nSurface area of the regular pyramid =550 sq. mm<\/p>\n<p>Explanation:<br \/>\nSurface area of the regular pyramid = A + (1\/2) ps<br \/>\narea = 30 +(1\/2) 20 x 26<br \/>\nsurface area = 30 + 520<br \/>\nsurface area = 550 sq. mm<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-15.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 15\" width=\"132\" height=\"147\" \/><br \/>\nAnswer:<br \/>\nSurface area of the regular pyramid =61 sq. cm<\/p>\n<p>Explanation:<br \/>\nSurface area of the regular pyramid = A + (1\/2) ps<br \/>\narea = 7 +(1\/2) 6 x 9<br \/>\nsurface area = 7 + 54<br \/>\nsurface area = 61 sq. cm<\/p>\n<p><strong>Find the selling price.<\/strong><br \/>\nQuestion 4.<br \/>\nCost to store: $75<br \/>\nMarkup: 20%<br \/>\nAnswer:<br \/>\nSelling price = 1665 $<\/p>\n<p>Explanation:<br \/>\nSelling price = cost to store x markup + cost to store<br \/>\nselling price = $75 x 20% + $75<br \/>\nselling price = $75x 0.20 + $75<br \/>\ns p = 1665 $<br \/>\nQuestion 5.<br \/>\nCost to store: $90<br \/>\nMarkup: 60%<br \/>\nAnswer:<br \/>\nSelling price = 5490$<\/p>\n<p>Explanation:<br \/>\nSelling price = cost to store x markup + cost to store<br \/>\nselling price = $90 x 60% + $90<br \/>\nselling price = $90x 0.60+ $90<br \/>\ns p = 5490 $<\/p>\n<p>Question 6.<br \/>\nCost to store: $130<br \/>\nMarkup: 85%<br \/>\nAnswer:<br \/>\nSelling price =10,530 $<\/p>\n<p>Explanation:<br \/>\nSelling price = cost to store x markup + cost to store<br \/>\nselling price = $130 x 85% + $130<br \/>\nselling price = $130 x 0.80+ $130<br \/>\ns p = 10,530$<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>USING TOOLS<\/strong> In the figure, each cube has a volume of 1 cubic unit. Find the volume of the figure and the area of its base. (See Exploration 1, p. 427.)<br \/>\nQuestion 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27555\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-16.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 16\" width=\"102\" height=\"90\" \/><br \/>\nAnswer:<br \/>\nThe volume of the cube = length + breadth + height<br \/>\n1 x 3 = 3<\/p>\n<p>Explanation:<br \/>\nThe volume of the cube = length + breadth + height<br \/>\nwhere length = l, width = w ,height = h<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27556\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-17.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 17\" width=\"111\" height=\"124\" \/><br \/>\nAnswer:<br \/>\nThe volume of the cube = length + breadth + height<br \/>\n1 x 4 = 4<\/p>\n<p>Explanation:<br \/>\nThe volume of the cube = length + breadth + height<br \/>\nwhere length = l, width = w ,height = h<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27557\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-18.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 18\" width=\"110\" height=\"80\" \/><br \/>\nAnswer:<br \/>\nThe volume of the cube = length + breadth + height<br \/>\n1 x 2 = 2<\/p>\n<p>Explanation:<br \/>\nThe volume of the cube = length + breadth + height<br \/>\nwhere length = l, width = w ,height = h<\/p>\n<p><strong>FINDING THE VOLUME OF A PRISM<\/strong> Find the volume of the prism.<br \/>\nQuestion 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27558\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-19.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 19\" width=\"119\" height=\"97\" \/><br \/>\nAnswer:<br \/>\nThe volume of the prism = 81 cu. in<\/p>\n<p>Explanation:<br \/>\nvolume v = B h<br \/>\nv = 9 x 9<br \/>\nv = 81 cu.in<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27559\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-20.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 20\" width=\"136\" height=\"104\" \/><br \/>\nAnswer:<br \/>\nThe volume of the prism = 48 cu. cm<\/p>\n<p>Explanation:<br \/>\nvolume v = B h<br \/>\nv = 6 x 8<br \/>\nv = 48 cu. cm<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27560\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-21.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 21\" width=\"115\" height=\"91\" \/><br \/>\nAnswer:<br \/>\nThe volume of the prism = 48 cu. m<\/p>\n<p>Explanation:<br \/>\nvolume v = B h<br \/>\nv = 7 x 8.5<br \/>\nv = 59.5 cu. m<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27561\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-22.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 22\" width=\"125\" height=\"94\" \/><br \/>\nAnswer:<\/p>\n<p>The volume of the prism = 48 cu. yd<\/p>\n<p>Explanation:<br \/>\nvolume v = B h<br \/>\nv = 8.33 x 6<br \/>\nv = 50 cu. yd<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27562\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-23.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 23\" width=\"95\" height=\"84\" \/><br \/>\nAnswer:<\/p>\n<p>The volume of the prism = 54 cu.ft<\/p>\n<p>Explanation:<br \/>\nvolume v = B h<br \/>\nv = 9 x 6<br \/>\nv = 54 cu.ft<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27563\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-24.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 24\" width=\"157\" height=\"93\" \/><br \/>\nAnswer:<\/p>\n<p>The volume of the prism = 84 cu.mm<\/p>\n<p>Explanation:<br \/>\nvolume v = B h<br \/>\nv = 10.5 x 8<br \/>\nv = 84 cu.mm<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27564\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-25.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 25\" width=\"145\" height=\"93\" \/><br \/>\nAnswer:<\/p>\n<p>The volume of the prism = 48 cu.m<\/p>\n<p>Explanation:<br \/>\nvolume v = B h<br \/>\nv = 10 x 4.8<br \/>\nv = 48 cu.m<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27565\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-26.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 26\" width=\"143\" height=\"111\" \/><br \/>\nAnswer:<\/p>\n<p>The volume of the prism = 645 cu. mm<\/p>\n<p>Explanation:<br \/>\nvolume v = B h<br \/>\nv = 15 x 43<br \/>\nv = 645 cu. mm<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27566\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-27.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 27\" width=\"106\" height=\"96\" \/><br \/>\nAnswer:<\/p>\n<p>The volume of the prism =3320 cu. feet<\/p>\n<p>Explanation:<br \/>\nvolume v = B h<br \/>\nv = 166 x 20<br \/>\nv = 3320 cu. ft<\/p>\n<p>Question 19.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds the volume of the triangular prism. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27567\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-28.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 28\" width=\"298\" height=\"122\" \/><br \/>\nAnswer:<br \/>\nYes my friend is correct.<\/p>\n<p>Explanation:<br \/>\nVolume of triangular prism = B h<br \/>\nvolume = 10 x (5 x 7)<br \/>\nvolume = 10 x (35)<br \/>\nvolume = 350 cubic centimeters<\/p>\n<p>Question 20.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA battery for an underwater drone is in the shape of a square prism. It is designed to draw in seawater that is then used to produce energy. The base of the battery has side lengths of 15 centimeters and the height of the battery is 10 centimeters. Find the volume of the battery.<br \/>\nAnswer:<br \/>\nThe volume of the battery\u00a0 = 2250 cu. centimeters.<\/p>\n<p>Explanation:<br \/>\nVolume of a square prism = a square h<br \/>\ngiven that a = 15 cm, h = 10 cm<br \/>\nvolume = 15 x 15x 10<br \/>\nvolume = 2250 cu. centimeters.<br \/>\nQuestion 21.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA cereal box has a volume of 225 cubic inches. The length of the base is 9 inches and the width of the base is 2.5 inches. What is the height of the box? Justify your answer.<br \/>\nAnswer:<br \/>\nThe heightt of the box = 10 inches.<\/p>\n<p>Explanation:<br \/>\nv = length x width x height<br \/>\nv = 225 cubic inches, l = 9 inches,w = 2.5 in<br \/>\n225 = 9 x 2.5 x h<br \/>\n225 = 22.5 h<br \/>\nh = 225\/22.5<br \/>\nh = 10 inches<\/p>\n<p>Question 22.<br \/>\n<strong>REASONING<\/strong><br \/>\nEach locker is shaped like a rectangular prism. Which has more storage space? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27568\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-29.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 29\" width=\"230\" height=\"224\" \/><br \/>\nAnswer:<br \/>\nThe school locker has the more storage space.<\/p>\n<p>Explanation:<br \/>\n2. The surface area of the rectangular prism = 2(lw + lh + wh)<br \/>\narea = 2(10 x 12) +(15 x 48) +(12 x 48) where l= 15 in,w = 12 in,h= 48 in<br \/>\narea = 2(120) +(720) +(576)<br \/>\narea = 2(1416)<br \/>\narea = 2832 sq. in<br \/>\n1. The surface area of the rectangular prism = 2(lw + lh + wh)<br \/>\narea = 2(15 x 12) +(10 x 60) +(12 x 60) where l= 10 in,w = 12 in,h= 60 in<br \/>\narea = 2(120) +(600) +(720)<br \/>\narea = 2(1440)<br \/>\narea = 2880 sq. in<\/p>\n<p>Question 23.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nHow many cubic inches are in 1 cubic foot? Use a sketch to explain your reasoning.<br \/>\nAnswer:<br \/>\n1 cubic foot = 1728 cubic inches.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34141\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-9-300x279.png\" alt=\"\" width=\"300\" height=\"279\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-9-300x279.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-9.png 310w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA concrete construction block has the measurements shown. How much concrete is used to make the block? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27569\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-30.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 30\" width=\"214\" height=\"125\" \/><br \/>\nAnswer:<br \/>\nThe concrete used to make the block = 544 sq. in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the rectangular prism = 2(lw + lh + wh)<br \/>\narea = 2(16 x 8) +(16 x 6) +(8 x 6) where l= 16in,w = 8 in,h= 6 in<br \/>\narea = 2(128) +(96) +(48)<br \/>\narea = 2(272)<br \/>\narea = 544 sq. in<\/p>\n<p>Question 25.<br \/>\n<strong>RESEARCH<\/strong><br \/>\nThe gas tank is 20% full. Use the current price of regular gasoline in your community to find the cost to fill the tank. (1 gal = 231 in.<sup>3<\/sup>)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27570\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-31.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 31\" width=\"295\" height=\"183\" \/><br \/>\nAnswer:<\/p>\n<p>Question 26.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nTwo liters of water are poured into an empty vase shaped like an octagonal prism. The base area is 100 square centimeters. What is the height of the water? (1 L = 1000 cm<sup>3<\/sup>)<br \/>\nAnswer:<br \/>\nThe height of the water = 20 centimeters<\/p>\n<p>Explanation:<br \/>\n1 liter = 1000 cubic centimeters.<br \/>\narea of the base = 100 square cm<br \/>\nheight = h<br \/>\nthe volume of water in the vase = 2 liters = 2000 cubic centimeters<br \/>\nthe volume of water in the vase = area of base x-height of the prism<br \/>\n2000 = 100 h<br \/>\nh = 20 cm<br \/>\nQuestion 27.<br \/>\n<strong>LOGIC<\/strong><br \/>\nTwo prisms have the same volume. Do they always, sometimes never, or have the same surface area? Justify your answer.<br \/>\nAnswer:<br \/>\nIf the volume is the same, they do not have the surface area.<\/p>\n<p>Explanation:<br \/>\nif we take two prisms at random that have the same volume, it&#8217;s very likely that they don&#8217;t have the same surface area.<\/p>\n<p>Question 28.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nHow many times greater is the volume of a triangular prism when one of its dimensions is doubled? when all three dimensions are doubled?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27571\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-10.4-32.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume 10.4 32\" width=\"137\" height=\"119\" \/><br \/>\nAnswer:<br \/>\nThe volume is 8 times greater when we double all 3 dimensions.<\/p>\n<p>Explanation:<br \/>\nwe are doubling only one dimension means that you are multiplying by 2 only 1 time.<\/p>\n<h3><a id=\"Lesson_10.5_Volumes_of_Pyramids\"><\/a>Lesson 10.5 Volumes of Pyramids<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Finding a Formula for the Volume of a Pyramid<br \/>\nWork with a partner. Draw the two nets on cardboard and cut them out. Fold and tape the nets to form an open cube and an open square pyramid. Both figures should have the same size square base and the same height.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27578\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 1\" width=\"479\" height=\"192\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-1.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-1-300x120.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\na. Compare the volumes of the figures. What do you notice?<br \/>\nb. Use your observations in part(a) to write a formula for the volume of a pyramid.<br \/>\nc. The rectangular prism below can be cut to form three pyramids. Use your formula in part(b) to show that the sum of the volumes of the three pyramids is equal to the volume of the prism.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27579\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 2\" width=\"641\" height=\"377\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-2.png 641w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-2-300x176.png 300w\" sizes=\"(max-width: 641px) 100vw, 641px\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = (1\/3) Bh<\/p>\n<p>Explanation:<br \/>\na. the volume of the pyramid =(1\/3) B h<br \/>\n1. v = (1\/3)\u00a0 x 2 x2<br \/>\nv = (1\/3) x 4<br \/>\nv = 1.33 in<\/p>\n<p>the volume of the pyramid =(1\/3) B h<br \/>\n1. v = (1\/3)\u00a0 x 2 x2.5<br \/>\nv = (1\/3) x 5<br \/>\nv = 1.66 in<br \/>\nb.\u00a0 the second figure has a greater volume than the 1st figure<br \/>\nc. the volume of the pyramid = (1\/3) B h<br \/>\nthe volume of the prism = Bh<br \/>\nThe volume of the 3 pyramids is equal to the volume of the prism.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the volume of the pyramid.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27580\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 3\" width=\"138\" height=\"151\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = 42 cubic feet<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nB = 21 square feet h= 6 ft<br \/>\nvolume = (1\/3) x 21&#215;6<br \/>\nvolume = (126\/3)<br \/>\nvolume = 42 cu. ft<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27581\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-4.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 4\" width=\"215\" height=\"118\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = 290 cubic centimeter<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nB =174 square cm h= 5 cm<br \/>\nvolume = (1\/3) x 174 x 5<br \/>\nvolume = (870\/3)<br \/>\nvolume = 290 cubic centimeter<\/p>\n<p><strong>Find the volume of the pyramid.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27582\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-5.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 5\" width=\"148\" height=\"92\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = 290 cubic centimeter<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nB =18 in h= 7 in<br \/>\nvolume = (1\/3) x 18x 7<br \/>\nvolume = (126\/3)<br \/>\nvolume = 42 inches<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27583\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-6.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 6\" width=\"186\" height=\"111\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = 91.66 square centimeter<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nB =25 cm h= 11 cm<br \/>\nvolume = (1\/3) x 25x 11<br \/>\nvolume = (275\/3)<br \/>\nvolume = 91.66 cm<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 5.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow is the formula for the volume of a pyramid different from the formula for the volume of a prism?<br \/>\nAnswer:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid h = height<br \/>\nthe volume of the prism = B h<br \/>\nwhere B = base of the prism h= height<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid\u00a0 is 3 times greater the volume of the prism.<\/p>\n<p>Question 6.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nHow many different pyramids can you draw with the same height and volume? Explain.<br \/>\nAnswer:<br \/>\nWe can draw the 2 or 3 pyramids with the same height and volume<\/p>\n<p>Explanation:<br \/>\nWe can draw the 2 or 3 pyramids with the same height and volume .<br \/>\nit is our wish to draw as many as possible<br \/>\n<strong>FINDING THE VOLUME OF A PYRAMID<\/strong> Find the volume of the pyramid.<br \/>\nQuestion 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27584\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-7.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 7\" width=\"123\" height=\"139\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = cubic yard<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B = 10 and h= 6<br \/>\nv = (1\/3) x 10 x 6<br \/>\nv = (60\/3)<br \/>\nv = 20 cubic yds<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27585\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-8.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 8\" width=\"107\" height=\"127\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = 12 cubic centimeters<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B = 4 and h= 9<br \/>\nv = (1\/3) x 4 x 9<br \/>\nv = (36\/3)<br \/>\nv = 12 cu. cm<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 9.<br \/>\nA resort features a square pyramid with a water slide. The length of the water slide is 90% of the height of the pyramid. The base of the pyramid has side lengths of 60 feet. The volume of the pyramid is 60,000 cubic feet. What is the length of the water slide?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27586\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-9.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 9\" width=\"167\" height=\"155\" \/><br \/>\nAnswer:<br \/>\nThe length of the water slide = 50 cubic feet<\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nTo make a candle, you use a mold to create the wax pyramid shown. You cut off the top 3 centimeters of the pyramid to make space for a wick. If the base area of the removed portion is 5.4 square centimeters, what percentage of the wax did you remove?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27587\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-10.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 10\" width=\"175\" height=\"136\" \/><br \/>\nAnswer:<br \/>\nThe percentage of the wax we remove = 140 cubic centimeters.<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nvolume = (1\/3) x 60 x 7<br \/>\nvolume =( 420\/3)<br \/>\nvolume = 140 cubic centimeters.<\/p>\n<h3><a id=\"Volumes_of_Pyramids_Homework_&amp;_Practice_10.5\"><\/a>Volumes of Pyramids Homework &amp; Practice 10.5<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the volume of the prism.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27588\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-11.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 11\" width=\"204\" height=\"105\" \/><br \/>\nAnswer:<br \/>\nThe volume of the prism = 189 cubic feets<\/p>\n<p>Explanation:<br \/>\nThe volume of the rectangular prism = l x w x h<br \/>\nv = 9 x 7 x 3<br \/>\nv = 189 cubic feets<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27589\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-12.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 12\" width=\"173\" height=\"103\" \/><br \/>\nAnswer:<br \/>\nThe volume of the prism = 189 cubic centimeters<\/p>\n<p>Explanation:<br \/>\nThe volume of the triangular prism = (b x h x l)\/ 2<br \/>\nv = (5 x 3 x 8)\/2<br \/>\nv = 60 cubic centimeters<\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><br \/>\nQuestion 3.<br \/>\nr + 0.5 &lt; &#8211; 0.4<br \/>\nAnswer:<br \/>\nr = &#8211; 0.9<\/p>\n<p>Explanation:<br \/>\nr = -0.4 -0.5<br \/>\nr = -0.9<\/p>\n<p>Question 4.<br \/>\nz &#8211; 2.4 \u2265 &#8211; 0.6<br \/>\nAnswer:<br \/>\nz = 1.8<\/p>\n<p>Explanation:<br \/>\nz = -0.6\u00a0 (+ 2.4)<br \/>\nz = 1.8<\/p>\n<p>Question 5.<br \/>\nh &#8211; 5 \u2264 &#8211; 3.7<br \/>\nAnswer:<br \/>\nh = -1.3<\/p>\n<p>Explanation:<br \/>\nh = -3.7 +5<br \/>\nh = -1.3<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>VOLUMES OF PYRAMIDS<\/strong> The rectangular prism is cut to form three pyramids. Show that the sum of the volumes of the three pyramids is equal to the volume of the prism. (See Exploration 1, p. 433.)<br \/>\nQuestion 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27590\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-13.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 13\" width=\"173\" height=\"104\" \/><br \/>\nAnswer:<br \/>\nThe volume of the\u00a0 3 pyramids is equal to the volume of the prism.<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B = 6 and h= 4<br \/>\nv = (1\/3) x 6 x 4<br \/>\nv = (24\/3)<br \/>\nv = 8 cubic feet<br \/>\nthe volume of the pyramid is 3 times greater than volume of the prism.<br \/>\nThe volume of the prism =\u00a0 B h<br \/>\nwhere B = base of the prism, h = height<br \/>\nv =\u00a0 B xh where B = 6 and h= 4<br \/>\nv =\u00a0 6 x 4<br \/>\nv = 24<br \/>\n8 x 3 = 24<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27591\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-14.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 14\" width=\"158\" height=\"126\" \/><br \/>\nAnswer:<br \/>\nThe volume of the\u00a0 3 pyramids is equal to the volume of the prism.<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B = 6 and h= 6<br \/>\nv = (1\/3) x 6 x 6<br \/>\nv = (36\/3)<br \/>\nv = 12 inches<br \/>\nthe volume of the pyramid is 3 times greater than volume of the prism.<br \/>\nThe volume of the prism=\u00a0 B h<br \/>\nwhere B = base of the prism, h = height<br \/>\nv =\u00a0 B xh where B = 6 and h= 6<br \/>\nv =\u00a0 6 x 6<br \/>\nv = 36 in<br \/>\n12 x 3 = 36<\/p>\n<p><strong>FINDING THE VOLUME OF A PYRAMID<\/strong> Find the volume of the pyramid.<br \/>\nQuestion 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27592\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-15.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 15\" width=\"119\" height=\"100\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid =\u00a0 0.66 cubic feet<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B = 1 and h= 2<br \/>\nv = (1\/3) x 1 x 2<br \/>\nv = (2\/3)<br \/>\nv = 0.66 cubic feet<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27593\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-16.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 16\" width=\"97\" height=\"109\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = 6.66\u00a0 cubic feet<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B = 2 and h= 10<br \/>\nv = (1\/3) x 10 x 2<br \/>\nv = (20\/3)<br \/>\nv = 6.66 cubic feet<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27594\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-17.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 17\" width=\"114\" height=\"109\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = 16\u00a0 cubic feet<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B = 8 and h= 7<br \/>\nv = (1\/3) x 8 x 7<br \/>\nv = (48\/3)<br \/>\nv = 16 cubic feet<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27595\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-18.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 18\" width=\"122\" height=\"111\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = 20\u00a0 cubic millimeters<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B = 15 mm and h= 4<br \/>\nv = (1\/3) x 15 x 4<br \/>\nv = (60\/3)<br \/>\nv = 20 cubic mm<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27596\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-19.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 19\" width=\"124\" height=\"127\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = 10.666 cu. yds<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B = 4 and h= 8<br \/>\nv = (1\/3) x 4 x 8<br \/>\nv = (32\/3)<br \/>\nv = 10.666 cu. yd<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27597\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-20.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 20\" width=\"135\" height=\"123\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = 36 cu. in<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B = 6 and h= 8<br \/>\nv = (1\/3) x 6 x 8<br \/>\nv = (48\/3)<br \/>\nv = 36 cu. in<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27598\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-21.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 21\" width=\"145\" height=\"104\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = 70 cu. mm<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B = 14 and h = 15 mm<br \/>\nv = (1\/3) x 14x 15<br \/>\nv = (210\/3)<br \/>\nv = 70 cu. mm<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27599\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-22.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 22\" width=\"115\" height=\"123\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = 2.333 cubic centimeters<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B = 1 and h = 7 cm<br \/>\nv = (1\/3) x 1 x 7<br \/>\nv = (7\/3)<br \/>\nv = 2.333 cubic centimeters<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27600\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-23.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 23\" width=\"128\" height=\"115\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = 252 cubic millimeters<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B = 63 and h = 12 mm<br \/>\nv = (1\/3) x 63 x 12<br \/>\nv = (756\/3)<br \/>\nv\u00a0 = 252 cubic millimeters<\/p>\n<p>Question 17.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds the volume of the pyramid. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27601\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-24.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 24\" width=\"301\" height=\"111\" \/><br \/>\nAnswer:<br \/>\nNo my friend is not correct.<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) x B x h<br \/>\nvolume = (8 x 4 x 7)\/3<br \/>\nvolume = (224\/3)<br \/>\nvolume = 74.666 cu. in<\/p>\n<p>Question 18.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA researcher develops a cage for a living cell in the shape of a square-based pyramid. A scale model of the cage is shown. What is the volume of the model?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27602\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-25.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 25\" width=\"178\" height=\"107\" \/><br \/>\nAnswer:<br \/>\nThe volume of the model = 133.33 cu. millimeters<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B = 20 and h = 20 mm<br \/>\nv = (1\/3) x 20 x 20<br \/>\nv = (400\/3)<br \/>\nv\u00a0 = 133.33 cu. millimeters<\/p>\n<p>Question 19.<br \/>\n<strong>FINDING VOLUME<\/strong><br \/>\nFind the volume of the composite solid. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27603\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-26.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 26\" width=\"159\" height=\"130\" \/><br \/>\nAnswer:<br \/>\nThe volume of the\u00a0 compositte solid =48 cu. feet<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B =36 and h = 4 ft<br \/>\nv = (1\/3) x 36 x 4<br \/>\nv = (144\/3)<br \/>\nv\u00a0 = 48 cu. feet<\/p>\n<p>Question 20.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nIn 1483, Leonardo da Vinci designed a parachute. It is believed that this was the first parachute ever designed. In a notebook, he wrote, \u201cIf a man is provided with a length of gummed linen cloth with a length of 12 yards on each side and 12 yards high, he can jump from any great height whatsoever without injury.\u201d Find the volume of air inside Leonardo\u2019s parachute.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27604\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-27.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 27\" width=\"196\" height=\"258\" \/><br \/>\nAnswer:<br \/>\nThe volume of the air inside parachute\u00a0 =48 cu. yd<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B =12 and h = 12<br \/>\nv = (1\/3) x 12 x 12<br \/>\nv = (144\/3)<br \/>\nv = 48 cu. yds<\/p>\n<p>Question 21.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nWhich sandcastle spire has a greater volume? How much more sand do you need to make the spire with the greater volume?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27605\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-28.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 28\" width=\"345\" height=\"128\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-28.png 345w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-28-300x111.png 300w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><br \/>\nAnswer:<br \/>\nspire B has greater volume<br \/>\n4 % of sand is needed to make the spire<\/p>\n<p>Explanation:<br \/>\nThe volume of the spire A = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B =30 and h = 6<br \/>\nv = (1\/3) x 30 x 6<br \/>\nv = (180\/3)<br \/>\nv = 60 in<br \/>\nThe volume of the spire B = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B =24 and h = 8<br \/>\nv = (1\/3) x 24 x 8<br \/>\nv = (192\/3)<br \/>\nv = 64 cu. in<\/p>\n<p>Question 22.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nUse the photo of the tepee.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27606\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-29.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 29\" width=\"267\" height=\"315\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-29.png 267w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-29-254x300.png 254w\" sizes=\"(max-width: 267px) 100vw, 267px\" \/><br \/>\na. What is the shape of the base? How can you tell?<br \/>\nb. The tepee\u2019s height is about 10 feet. Estimate the volume of the tepee.<br \/>\nAnswer:<br \/>\na. The shape of the base is a triangular pyramid .<br \/>\nb . The volume of the triangular pyramid = 3.33<\/p>\n<p>Explanation:<br \/>\nb . The volume of the triangular pyramid = (1\/3) B h<br \/>\nvolume = (1\/3) B 10<br \/>\nvolume = (10 b \/3)<br \/>\n10 B = 3<br \/>\nB = (10\/3)<br \/>\nB = 3.33<\/p>\n<p>Question 23.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nA rectangular pyramid has a volume of 40 cubic feet and a height of 6 feet. Find one possible set of dimensions of the base.<br \/>\nAnswer:<br \/>\nThe dimensions of the base = 20 feet<\/p>\n<p>Explanation:<br \/>\nThe volume of the rectangular pyramid = (1\/3) xB x h<br \/>\nvolume = (1\/3) x B x 6 where h = 6 ,v= 40 given<br \/>\n40 = (1\/3) x 6 B<br \/>\n2 B = 40<br \/>\nB = 20\u00a0 feet<\/p>\n<p>Question 24.<br \/>\n<strong>REASONING<\/strong><br \/>\nDo the two solids have the same volume? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27607\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-10-Surface-Area-and-Volume-10.5-30.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 10 Surface Area and Volume 10.5 30\" width=\"268\" height=\"78\" \/><br \/>\nAnswer:<br \/>\nNo, the two solids did not have the same volume.<\/p>\n<p>Explanation:<br \/>\nThe volume of rectangular prism = l wh<br \/>\nvolume = xyz<br \/>\nThe volume of the triangular prism = b hl\/2<br \/>\nvolume = (xy3z\/2)<\/p>\n<h3><a id=\"Lesson_10.6_Cross_Sections_of_Three-Dimensional_Figures\"><\/a>Lesson 10.6 Cross Sections of Three-Dimensional Figures<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Describing Cross Sections<br \/>\nWork with a partner. A baker is thinking of different ways to slice zucchini bread that is in the shape of a rectangular prism. The shape that is formed by the cut is called a cross section.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27608\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-1.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 1\" width=\"257\" height=\"127\" \/><br \/>\na. What is the shape of the cross section when the baker slices the bread vertically, as shown above?<br \/>\nb. What is the shape of the cross section when the baker slices the bread horizontally?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27609\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-2.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 2\" width=\"171\" height=\"116\" \/><br \/>\nc. What is the shape of the cross section when the baker slices off a corner of the bread?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27610\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-3.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 3\" width=\"485\" height=\"163\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-3.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-3-300x101.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\nd. Is it possible to obtain a cross section that is a trapezoid? Explain.<br \/>\ne. Name at least 3 cross sections that are possible to obtain from a rectangular pyramid. Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Consider a plane \u201cslicing\u201d through a solid. The intersection of the plane and the solid is a two-dimensional shape called a cross section. For example, the diagram shows that the intersection of the plane and the rectangular prism is a rectangle.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-27611\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-4.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 4\" width=\"434\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-4.png 434w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-4-300x99.png 300w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Describe the intersection of the plane and the solid.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27612\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-5.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 5\" width=\"127\" height=\"126\" \/><br \/>\nAnswer:<br \/>\nThe intersection of the plane of the solid = one dimensional<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27613\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-6.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 6\" width=\"160\" height=\"130\" \/><br \/>\nAnswer:<br \/>\nThe intersection of the plane of the solid = two dimensional<\/p>\n<p><strong>Describe the intersection of the plane and the solid.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27614\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-7.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 7\" width=\"203\" height=\"88\" \/><br \/>\nAnswer:<br \/>\nThe intersection of the plane of the cylinder = two dimensional<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27615\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-8.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 8\" width=\"110\" height=\"120\" \/><br \/>\nAnswer:<br \/>\nThe intersection of the plane of the cone = two dimensional<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 5.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat is a cross section?<br \/>\nAnswer:<br \/>\nThe intersection of the plane of the solid is a two-dimensional is called crosssection.<br \/>\nQuestion 6.<br \/>\n<strong>DESCRIBING CROSS SECTIONS<\/strong><br \/>\nDescribe the intersection of the plane and the solid at the left.<br \/>\nAnswer:<br \/>\nThe intersection of the plane and the solid at the left is a two dimensional.<\/p>\n<p>Question 7.<br \/>\n<strong>REASONING<\/strong><br \/>\nName all possible cross sections of a cylinder.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27616\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-9.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 9\" width=\"107\" height=\"156\" \/><br \/>\nAnswer:<br \/>\nThe cross-section of the sphere is a circle. The vertical cross-section of a cone is a triangle, and the horizontal cross- section is a circle.<\/p>\n<p>Question 8.<br \/>\n<strong>WHICH ONE DOESN&#8217;T BELONG?<\/strong><br \/>\nYou slice a square prism. Which cross section does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27617\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-10.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 10\" width=\"374\" height=\"46\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-10.png 374w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-10-300x37.png 300w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/><br \/>\nAnswer:<br \/>\ncircle crosssection does not belong with the other three.<\/p>\n<p>Explanation:<br \/>\nsquare, triangle, the rectangle does not belong with the three.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 9.<br \/>\nA steel beam that is 12 meters long is cut into four equal parts. The cross sections are rectangles with side lengths of 1 meter and 2 meters.<br \/>\na. What is the perimeter of each cross section?<br \/>\nb. What is the area of each cross section?<br \/>\nc. What is the volume of the original beam?<br \/>\nAnswer:<br \/>\na. The perimeter of each cross-section =\u00a0 3 meters<br \/>\nb. The area of each cross-section = 2 meters<br \/>\nc.\u00a0 The volume of the original beam = 12 meters.<\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA lumberjack saws a cylindrical tree trunk at an angle. Is the cross-section a circle? Explain your reasoning.<br \/>\nAnswer:<br \/>\nYes, the cross-section is a circle.<\/p>\n<p>Explanation:<br \/>\nThe cross-section of the sphere is a circle<\/p>\n<h3><a id=\"Cross_Sections_of_Three-Dimensional_Figures_Homework_&amp;_Practice_10.6\"><\/a>Cross Sections of Three-Dimensional Figures Homework &amp; Practice 10.6<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the volume of the pyramid.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27618\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-11.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 11\" width=\"123\" height=\"100\" \/><br \/>\nAnswer:<br \/>\nThe volume of the\u00a0 pyramid = 37.33 cu. in<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B =16 and h = 7 in<br \/>\nv = (1\/3) x16 x 7<br \/>\nv = (112\/3)<br \/>\nv = 37.33 cu. in<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27619\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-12.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 12\" width=\"106\" height=\"112\" \/><br \/>\nAnswer:<br \/>\nThe volume of the\u00a0 pyramid = 2.875 cubic centimeters.<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nwhere B = base of the pyramid, h = height<br \/>\nv = (1\/3) x B xh where B =23 and h = 8<br \/>\nv = (1\/3) x23 x 8<br \/>\nv = (112\/3)<br \/>\nv = 2.875 cubic centimeters.<\/p>\n<p><strong>Find the sum.<\/strong><br \/>\nQuestion 3.<br \/>\n(w &#8211; 7) + (- 6w &#8211; 5)<br \/>\nAnswer:<br \/>\nw = -2<\/p>\n<p>Explanation:<br \/>\nw = -11w+7<br \/>\nw=-4w<br \/>\n2w = -4<br \/>\nw= -2<\/p>\n<p>Question 4.<br \/>\n(8 &#8211; b) + (5b + 6)<br \/>\nAnswer:<br \/>\nb = 2.33<\/p>\n<p>Explanation:<br \/>\n-b = 5b-2<br \/>\n5b + 6b = 2<br \/>\nb = 2.33<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>DESCRIBING CROSS SECTIONS<\/strong> Determine whether it is possible to obtain the cross section from a cube. (See Exploration 2, p. 439.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27620\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-13.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 13\" width=\"118\" height=\"106\" \/><br \/>\nQuestion 5.<br \/>\ncircle<br \/>\nAnswer:<br \/>\nNo it is not possible to obtain the crosssection from a cube.<\/p>\n<p>Question 6.<br \/>\nsquare<br \/>\nAnswer:<br \/>\nNo it is not possible to obtain the crosssection from a cube.<\/p>\n<p>Question 7.<br \/>\nequilateral triangle<br \/>\nAnswer:<br \/>\nNo it is not possible to obtain the crosssection from a cube.<\/p>\n<p>Explanation:<br \/>\nequilateral triangle is not possible to obtain the crosssection from a cube.<\/p>\n<p>Question 8.<br \/>\npentagon<br \/>\nAnswer:<br \/>\nNo it is not possible to obtain the crosssection from a cube.<\/p>\n<p>Explanation:<br \/>\npentagon is not possible to obtain the crosssection from a cube.<\/p>\n<p>Question 9.<br \/>\nnon-rectangular parallelogram<br \/>\nAnswer:<br \/>\nNo it is not possible to obtain the crosssection from a cube.<\/p>\n<p>Explanation:<br \/>\nnon rectangular parallelogram is not possible to obtain the crosssection from a cube.<\/p>\n<p>Question 10.<br \/>\noctagon<br \/>\nAnswer:<br \/>\nNo it is not possible to obtain the crosssection from a cube.<\/p>\n<p>Explanation:<br \/>\noctagon is not possible to obtain the crosssection from a cube.<\/p>\n<p><strong>DESCRIBING CROSS SECTIONS OF PRISMS AND PYRAMIDS<\/strong> Describe the intersection of the plane and the solid.<br \/>\nQuestion 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27621\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-14.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 14\" width=\"160\" height=\"79\" \/><br \/>\nAnswer:<br \/>\nThe intersection of the prism and the solid is a two dimensional.<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27622\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-15.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 15\" width=\"113\" height=\"135\" \/><br \/>\nAnswer:<br \/>\nThe intersection of the pyramid and the solid is a one dimensional.<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27623\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-16.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 16\" width=\"152\" height=\"118\" \/><br \/>\nAnswer:<br \/>\nThe intersection of the pyramid and the solid is a two dimensional.<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27624\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-17.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 17\" width=\"157\" height=\"108\" \/><br \/>\nAnswer:<br \/>\nThe intersection of the pyramid and the solid is a three dimensional.<\/p>\n<p><strong>DESCRIBING CROSS SECTIONS OF CYLINDERS AND CONES<\/strong> Describe the intersection of the plane and the solid.<br \/>\nQuestion 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27625\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-18.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 18\" width=\"131\" height=\"90\" \/><br \/>\nAnswer:<br \/>\nThe intersection of the plane and the solid is a circle<\/p>\n<p>Explanation:<br \/>\nThe cross section of the cylinder is a circle.<br \/>\nQuestion 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27626\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-19.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 19\" width=\"147\" height=\"108\" \/><br \/>\nAnswer:<br \/>\nThe intersection of the plane and the solid is a circle<\/p>\n<p>Explanation:<br \/>\nThe cross section of the cone is a circle.<\/p>\n<p><strong>DESCRIBING CROSS SECTIONS<\/strong> Describe the shape that is formed by the cut in the food.<br \/>\nQuestion 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27627\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-20.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 20\" width=\"163\" height=\"106\" \/><br \/>\nAnswer:<br \/>\nThe shape that is formed is circle.<\/p>\n<p>Explanation:<br \/>\nThe cross section when it is cut it is formed a circle.<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27628\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-21.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 21\" width=\"150\" height=\"90\" \/><br \/>\nAnswer:<br \/>\nThe shape that is formed is semi-circle.<\/p>\n<p>Explanation:<br \/>\nThe cross section when it is cut it is formed a semi circle.<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27629\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-22.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 22\" width=\"149\" height=\"93\" \/><br \/>\nAnswer:<br \/>\nThe shape that is formed is\u00a0 circle.<\/p>\n<p>Explanation:<br \/>\nThe cross section when it is cut it is formed\u00a0 circle.<\/p>\n<p>Question 20.<br \/>\n<strong>DESCRIBING CROSS SECTIONS<\/strong><br \/>\nDescribe the intersection of the plane and the cylinder.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27630\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-23.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 23\" width=\"189\" height=\"119\" \/><br \/>\nAnswer:<br \/>\nThe intersection of a plane and a cylinder is a rectangle.<\/p>\n<p><strong>REASONING<\/strong> Determine whether the given intersection is possible. If so, draw the solid and the cross section.<br \/>\nQuestion 21.<br \/>\nThe intersection of a plane and a cone is a rectangle.<br \/>\nAnswer:<br \/>\nNo the intersection of a plane and a cone is a circle.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27626\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-19.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 19\" width=\"147\" height=\"108\" \/><br \/>\nQuestion 22.<br \/>\nThe intersection of a plane and a square pyramid is a triangle.<br \/>\nAnswer:<br \/>\nYes the intersection of a plane and a square pyramid is a triangle.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27612\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-5.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 5\" width=\"127\" height=\"126\" \/><\/p>\n<p>Question 23.<br \/>\n<strong>REASONING<\/strong><br \/>\nA plane that intersects a prism is parallel to the bases of the prism. Describe the intersection of the plane and the prism.<br \/>\nAnswer:<br \/>\nwhen a plane intersects a prism and is parallel to the bases of the prism , the intersection is the same shape as the base.<\/p>\n<p>Question 24.<br \/>\n<strong>REASONING<\/strong><br \/>\nExplain how a plane can be parallel to the base of a cone and intersect the cone at exactly one point.<br \/>\nAnswer:<br \/>\nA plane will be parallel to the base and intersecting the cone at only one point is only possible when the plana will pass through<\/p>\n<p>Question 25.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nAn artist plans to paint bricks.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27631\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-24.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 24\" width=\"172\" height=\"102\" \/><br \/>\na. Find the surface area of the brick.<br \/>\nb. The artist cuts along the length of the brick to form two bricks, each with a width of 2 inches. What is the percent of increase in the surface area? Justify your answer.<br \/>\nAnswer:<br \/>\na. The surface area of the brick = 164 in<br \/>\nb. The surface area of the percent increase = 2 %<\/p>\n<p>Explanation:<br \/>\nb.The surface area of the rectangular prism = 2(lw +lh +wh)<br \/>\nsurface area = 2(12 x 6 +12 x5\u00a0 +6 x 5)<br \/>\nsurface area = 2(72 + 60+30)<br \/>\nsurface area = 2(162)<br \/>\nsurface area = 81 in<br \/>\na. The surface area of the rectangular prism = 2(lw +lh +wh)<br \/>\nsurface area = 2(10 x 4 +10 x3 +4 x 3)<br \/>\nsurface area = 2(40 + 30 +12)<br \/>\nsurface area = 2(82)<br \/>\nsurface area = 164 in<br \/>\nQuestion 26.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA cross section of an artery is shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27633\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-25.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 25\" width=\"151\" height=\"110\" \/><br \/>\na. Describe the cross section of the artery.<br \/>\nb. The radius of the artery is 0.22 millimeter. What is the circumference of the artery?<br \/>\nAnswer:<br \/>\na. The cross section of the artery is a circle.<br \/>\nb. The circumference of the artery = 1.3816 millimeters<\/p>\n<p>Explanation:<br \/>\nThe circumference of the circle = 2\u03c0r<br \/>\nwhere r= 0.22 mm given \u03c0 = 3.14<br \/>\ncircumference = 2 x 3.14 x 0.22<br \/>\ncircumference= 1.3816 millimeters<\/p>\n<p>Question 27.<br \/>\n<strong>REASONING<\/strong><br \/>\nThree identical square pyramids each with a height of meters and a base area of 100 square meters are shown. For each pyramid, a cross section parallel to the base is shown. Describe the relationship between the area of the base and the area of any cross section parallel to the base.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27634\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-26.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 10 Surface Area and Volume 10.6 26\" width=\"398\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-26.png 398w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-10-Surface-Area-and-Volume-10.6-26-300x102.png 300w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><br \/>\nAnswer:<br \/>\nThe relationship between the area of the base and the area of any cross section parallel to the base\u00a0 for 1st figure = 1: 2 %<br \/>\nThe relationship between the area of the base and the area of any cross section parallel to the base\u00a0 for 2nd figure = 1: 5%<br \/>\nThe relationship between the area of the base and the area of any cross section parallel to the base\u00a0 for 3rd figure = 1: 10%<\/p>\n<p>Explanation:<br \/>\nIn the above 3 figures\u00a0 the base area is same for all the 3 figures = 100 square meters<\/p>\n<h3><a id=\"Surface_Area_and_Volume_Connecting_Concepts\"><\/a>Surface Area and Volume Connecting Concepts<\/h3>\n<p><strong>Using the Problem-Solving Plan<\/strong><br \/>\nQuestion 1.<br \/>\nA store pays $2 per pound for popcorn kernels. One cubic foot of kernels weighs about 45 pounds. Wha tis the selling price of the container shown when the markup is 30%?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27635\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cc-1.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cc 1\" width=\"146\" height=\"175\" \/><br \/>\nUnderstand the problem.<br \/>\nYou are given the dimensions of a container of popcorn kernels and the price that a store pays for the kernels. You also know the weight of one cubic foot of popcorn kernels. You are asked to find the selling price of the container when the markup is 30%.<br \/>\nMake a plan.<br \/>\nUse the volume of the container to find the weight of the kernels. Then use the weight of the kernels to find the cost to the store. Finally, use the percent markup to find the selling price of the container.<br \/>\nSolve and check.<br \/>\nUse the plan to solve the problem. Then check your solution.<br \/>\nAnswer:<br \/>\nSelling price = 525 $<\/p>\n<p>Explanation:<br \/>\nSelling price = cost to store x markup + cost to store<br \/>\nselling price = $2 x 30% + $45<br \/>\nselling price = $2x 0.30 + $45<br \/>\nselling price = $525<\/p>\n<p>Question 2.<br \/>\nThe pyramid shown has a square base. What is the height of the pyramid? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27636\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cc-2.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cc 2\" width=\"123\" height=\"150\" \/><br \/>\nAnswer:<br \/>\nThe height of the pyramid = 3000 cm<\/p>\n<p>Explanation:<br \/>\nThe volume of the triangular pyramid = (1\/3) x B h<br \/>\n1500 = (1\/3) x 1.5 h<br \/>\n1500 = 0.5 h<br \/>\nh = (1500\/3)<br \/>\nh = 3000 cm<\/p>\n<p>Question 3.<br \/>\nA cylindrical can of soup has a height of 7 centimeters and a lateral surface area of 63\u03c0 square centimeters. The can is redesigned to have a lateral surface area of 45\u03c0 square centimeters without changing the radius of the can. What is the height of the new design? Justify your answer.<br \/>\nAnswer:<br \/>\nThe height of the new design can = 5 centimeters.<\/p>\n<p>Explanation:<br \/>\nThe can when it is redesigned to have a lateral surface area of 45\u03c0 = 5 x 9 = 45<br \/>\nThe height of the can when it is redesigned = 5 centimeters.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Volumes and Surface Areas of Small Objects<br \/>\nAt the beginning of this chapter, you watched a STEAM Video called \u201cPaper Measurements.\u201d You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27637\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cc-3.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cc 3\" width=\"362\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cc-3.png 362w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cc-3-300x149.png 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><\/p>\n<h3><a id=\"Surface_Area_and_Volume_Chapter_Review\"><\/a>Surface Area and Volume Chapter Review<\/h3>\n<p><strong>Review Vocabulary<\/strong><br \/>\nWrite the definition and give an example of each vocabulary term.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27638\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-1.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 1\" width=\"417\" height=\"50\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-1.png 417w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-1-300x36.png 300w\" sizes=\"(max-width: 417px) 100vw, 417px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><br \/>\nInformation Frame You can use an to help organize and remember a concept. Here is an example of an Information Frame for Surface Areas of Rectangular Prisms.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27639\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-2.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 2\" width=\"479\" height=\"382\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-2.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-2-300x239.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p>Choose and complete a graphic organizer to help you study the concept.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27640\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-3.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 3\" width=\"273\" height=\"285\" \/><br \/>\n1. surface areas of prisms<br \/>\n2. surface areas of cylinders<br \/>\n3. surface areas of pyramids<br \/>\n4. volumes of prisms<br \/>\n5. volumes of pyramids<br \/>\n6. cross sections of three-dimensional figures<\/p>\n<p><strong>Chapter Self-Assessment<\/strong><br \/>\nAs you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27641\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-4.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 4\" width=\"588\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-4.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-4-300x38.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p><strong>10.1 Surface Areas of Prisms (pp. 409\u2013414)<\/strong><br \/>\nLearning Target: Find the surface area of a prism.<\/p>\n<p>Find the surface area of the prism.<br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27642\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-5.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 5\" width=\"147\" height=\"92\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the Rectangular prism = 158 sq. in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the Rectangular prism = 2(lw + lh +wh)<br \/>\nwhere l = 8 w = 3 h = 5<br \/>\nrectangular prism =2(8 x 3) +(8 x 5) +(3 x 5)<br \/>\nprism = 2(24) + (40) +(15)<br \/>\nsurface area =2(79)<br \/>\nsurface area = 158 sq. in<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27643\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-6.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 6\" width=\"117\" height=\"84\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the triangular prism = 562 sq. cm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular prism = 2lw + 2lh + 2wh<br \/>\nsurface area = 2(7 x 8) + 2(8 x 15) +2(15&#215;7) where l = 8m,w = 8m, h= 8m<br \/>\nsurface area = 2(56) + 2(120)+ 2(105)<br \/>\nsurface area =112 + 240 + 210<br \/>\nsurface area = 562 sq. cm<br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27644\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-7.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 7\" width=\"97\" height=\"120\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the triangular prism = 262 sq. m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the triangular prism = 2lw + 2lh + 2wh<br \/>\nsurface area = 2(5 x 7) + 2(5x 8) +2(8&#215;7) where l = 5m,w = 7m, h= 8m<br \/>\nsurface area = 2(35) + 2(40)+ 2(56)<br \/>\nsurface area =70 + 80 + 112<br \/>\nsurface area = 262 sq. m<\/p>\n<p>Question 4.<br \/>\nYou want to wrap the box using a piece of wrapping paper that is 76 centimeters long by56 centimeters wide. Do you have enough wrapping paper to wrap the box? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27645\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-8.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 8\" width=\"165\" height=\"62\" \/><br \/>\nAnswer:<br \/>\nThe enough wrapping\u00a0 paper to wrap the box = 4180 cm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the Rectangular prism = 2(lw + lh +wh)<br \/>\nwhere l = 35 w = 50 h = 4<br \/>\nrectangular prism =2(35 x 50) +(50 x 4) +(35 x 4)<br \/>\nprism = 2(1750) + (200) +(140)<br \/>\nsurface area =2(2090)<br \/>\nsurface area = 4180 sq. cm<\/p>\n<p>Question 5.<br \/>\nTo finish a project, you need to paint the lateral surfaces of a cube with side length 2.5 inches. Find the area that you need to paint.<br \/>\nAnswer:<\/p>\n<p><strong>10.2 Surface Areas of Cylinders (pp. 415\u2013420)<\/strong><br \/>\nLearning Target: Find the surface area of a cylinder.<\/p>\n<p>Find the surface area and lateral surface area of the cylinder. Round your answers to the nearest tenth.<br \/>\nQuestion 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27646\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-9.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 9\" width=\"130\" height=\"145\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the cylinder = 169.56 square yards<br \/>\nThe lateral surface area of the cylinder = 113.04 square yards<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere\u00a0 radius = 3\u00a0 , height = 6\u00a0 given<br \/>\nsurface area = 2 x 3.14 x 3 x 3 + 2 x 3.14 x 3 x 6<br \/>\nsurface area =\u00a0 56.52+ 113.04<br \/>\nsurface area = 169.56<br \/>\nThe lateral surface area of the cylinder =\u00a0 2\u03c0rh<br \/>\nwhere\u00a0 radius = 3\u00a0 , height = 6\u00a0 given<br \/>\nsurface area =\u00a0 2 x 3.14 x 3 x 6<br \/>\nsurface area = 113.04 sq. yards<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27647\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-10.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 10\" width=\"240\" height=\"93\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the cylinder = 34.196 square centimeters<br \/>\nThe lateral surface area of the cylinder =30.144 square centimeters<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere\u00a0 radius = 0.8\u00a0 , height = 6\u00a0 given<br \/>\nsurface area = 2 x 3.14 x 0.8 x 0.8 + 2 x 3.14 x 0.8 x 6<br \/>\nsurface area =\u00a0 4.0192+ 30.144<br \/>\nsurface area = 34.196 square centimeters<br \/>\nThe lateral surface area of the cylinder =\u00a0 2\u03c0rh<br \/>\nwhere\u00a0 radius = 0.8\u00a0 , height = 6\u00a0 given<br \/>\nsurface area =\u00a0 2 x 3.14 x 0.8 x 6<br \/>\nsurface area = 30.144 square centimeters<\/p>\n<p>Question 8.<br \/>\nThe label covers the entire lateral surface area of the can. How much of the can is not covered by the label?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27648\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-11.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 11\" width=\"158\" height=\"151\" \/><br \/>\nAnswer:<br \/>\nThe can that is not covered =276.32 square centimeters<\/p>\n<p>Explanation:<br \/>\nThe lateral surface area of the cylinder =\u00a0 2\u03c0rh<br \/>\nwhere\u00a0 radius = 4 , height = 11\u00a0 given<br \/>\nsurface area =\u00a0 2 x 3.14 x 4 x11<br \/>\nsurface area = 276.32 square centimeters<\/p>\n<p><strong>10.3 Surface Areas of Pyramids (pp. 421\u2013426)<\/strong><br \/>\nLearning Target: Find the surface area of a pyramid.<\/p>\n<p>Find the surface area of the regular pyramid.<br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27649\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-12.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 12\" width=\"123\" height=\"119\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the pyramid =\u00a0 5 square inches.<\/p>\n<p>Explanation:<br \/>\nThe surface area of the pyramid = A + (1\/2) ps<br \/>\nsurface area = 2 +(1\/2) x 3 x 2<br \/>\nsurface area= 2 +3<br \/>\nsurface area= 5 sq. in<br \/>\nQuestion 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27650\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-13.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 13\" width=\"99\" height=\"121\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the pyramid =\u00a0 42.5 sq. meters<\/p>\n<p>Explanation:<br \/>\nThe surface area of the pyramid = A + (1\/2) ps<br \/>\nsurface area = 8 +(1\/2) x 10 x 6.9<br \/>\nsurface area= 8 +34.5<br \/>\nsurface area= 42.5 sq. m<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27651\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-14.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 14\" width=\"154\" height=\"128\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the pyramid = 115.8 sq. cm<\/p>\n<p>Explanation:<br \/>\nThe surface area of the pyramid = A + (1\/2) ps<br \/>\nsurface area = 84.3+(1\/2) x 9 x 7<br \/>\nsurface area= 84.3 +31.5<br \/>\nsurface area= 115.8\u00a0 sq. cm<\/p>\n<p>Question 12.<br \/>\nThe tent is shaped like a square pyramid. There is no fabric covering the ground.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27652\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-15.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 15\" width=\"116\" height=\"153\" \/><br \/>\na. Estimate the amount of fabric needed to make the tent.<br \/>\nb. Fabric costs $5.25 per square yard. How much will it cost to make the tent?<br \/>\nAnswer:<br \/>\na. The amount of fabric needed to make the tent = 12 ft<br \/>\nb. The cost to make the tent =<\/p>\n<p>Explanation:<br \/>\nThe surface area of the pyramid = A + (1\/2) ps<br \/>\nsurface area = 3+(1\/2) x 3 x 6<br \/>\nsurface area= 3 +9<br \/>\nsurface area= 12 sq. ft<\/p>\n<p><strong>10.4 Volumes of Prisms (pp. 427\u2013432)<\/strong><br \/>\nLearning Target: Find the volume of a prism.<\/p>\n<p>Find the volume of the prism.<br \/>\nQuestion 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27653\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-16.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 16\" width=\"111\" height=\"89\" \/><br \/>\nAnswer:<br \/>\nThe volume of prism = 96 cu. in<\/p>\n<p>Explanation:<br \/>\nThe volume of prism = lwh<br \/>\nwhere l = 8,w=2,h = 6<br \/>\nvolume = 8 x 2 x 6<br \/>\nvolume = 96 cu. in<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27654\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-17.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 17\" width=\"119\" height=\"100\" \/><br \/>\nAnswer:<br \/>\nThe volume of prism = 240 cu. m<\/p>\n<p>Explanation:<br \/>\nThe volume of prism =( lbh\/2)<br \/>\nwhere l = 4,w=8,h = 7.5<br \/>\nvolume = 8 x 4 x 7.5<br \/>\nvolume = 240 cu. m<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27655\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-18.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 18\" width=\"176\" height=\"106\" \/><br \/>\nAnswer:<br \/>\nThe volume of prism =607.5 cu. mm<\/p>\n<p>Explanation:<br \/>\nThe volume of prism = lwh<br \/>\nwhere l = 15,w=4.5,h = 9<br \/>\nvolume = 15 x 4.5 x 9<br \/>\nvolume = 607.5 cu. mm<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27656\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-19.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 19\" width=\"158\" height=\"100\" \/><br \/>\nAnswer:<br \/>\nThe volume of prism =96 cu. m<\/p>\n<p>Explanation:<br \/>\nThe volume of prism = lwh<br \/>\nwhere l = 6,w=3,h = 4<br \/>\nvolume = 6 x 3 x 4<br \/>\nvolume = 96 cu. m<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27657\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-20.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 20\" width=\"150\" height=\"122\" \/><br \/>\nAnswer:<br \/>\nThe volume of prism = 15.6 cu. cm<\/p>\n<p>Explanation:<br \/>\nThe volume of prism = lwh<br \/>\nwhere l = 2.6 ,w=1.5 ,h = 4<br \/>\nvolume = 2.6 x1.5 x 4<br \/>\nvolume = 15.6 cu. cm<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27658\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-21.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 21\" width=\"190\" height=\"114\" \/><br \/>\nAnswer:<br \/>\nThe volume of prism = 105 cubic feet<\/p>\n<p>Explanation:<br \/>\nThe volume of prism =( lbh\/2)<br \/>\nwhere l = 7 ,w=5 ,h = 3<br \/>\nvolume = 7 x 5 x 3<br \/>\nvolume = 105 cu. feet<\/p>\n<p>Question 19.<br \/>\nTwo cereal boxes each hold exactly 192 cubic inches of cereal. Which box should a manufacturer choose to minimize the amount of cardboard needed to make the cereal boxes?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27659\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-22.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 22\" width=\"237\" height=\"149\" \/><br \/>\nAnswer:<br \/>\nThe first cereal box is used to minimize<\/p>\n<p><strong>10.5 Volumes of Pyramids (pp.433-438)<\/strong><br \/>\nLearning Target: Find the volume of a pyramid.<\/p>\n<p>Find the volume of the pyramid.<br \/>\nQuestion 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27660\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-23.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 23\" width=\"126\" height=\"108\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = 133.33 cu. ft<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nvolume = (1\/3) 17 20<br \/>\nvolume = (340\/3)<br \/>\nvolume = 113.33 cu. ft<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27661\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-24.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 24\" width=\"107\" height=\"137\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = 2100 cubic in<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nvolume = (1\/3) 210 x\u00a0 30<br \/>\nvolume = (6300\/3)<br \/>\nvolume = 2100 cubic in<\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27662\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-25.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 25\" width=\"158\" height=\"115\" \/><br \/>\nAnswer:<br \/>\nThe volume of the pyramid = 48 cu. mm<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nvolume = (1\/3) 16 x\u00a0 9<br \/>\nvolume = (144\/3)<br \/>\nvolume =48 cu. mm<\/p>\n<p>Question 23.<br \/>\nA pyramid-shaped hip roof is a good choice for a house in an area with many hurricanes.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27663\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-26.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 26\" width=\"158\" height=\"150\" \/><br \/>\na. What is the volume of the roof to the nearest tenth of a foot?<br \/>\nb. What is the volume of the entire house, including the roof?<br \/>\nAnswer:<br \/>\na. The volume of the pyramid = 800 cu. ft<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nvolume = (1\/3) 80 x\u00a0 30<br \/>\nvolume = (2400\/3)<br \/>\nvolume =800 cu. ft<br \/>\nb.<br \/>\nThe volume of the pyramid = 400 cu. ft<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nvolume = (1\/3) 40 x\u00a0 30<br \/>\nvolume = (1200\/3)<br \/>\nvolume =400 cu. ft<\/p>\n<p>Question 24.<br \/>\nA laboratory creates calcite crystals for use in the study of light. The crystal is made up of two pieces of calcite that form a square pyramid. The base length of the top piece is 2 inches.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27664\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-27.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 27\" width=\"182\" height=\"127\" \/><br \/>\na. Find the volume of the entire pyramid.<br \/>\nb. Find the volume of each piece of the pyramid.<br \/>\nAnswer:<br \/>\na. The volume of the entire pyramid = 1.58 cu. in<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nvolume = (1\/3) 3.5 x\u00a0 3<br \/>\nvolume = (4.75\/3)<br \/>\nvolume =1.58 cu. in<br \/>\nb.The volume of the pyramid = 1.458 cu. in<\/p>\n<p>Explanation:<br \/>\nThe volume of the pyramid = (1\/3) B h<br \/>\nvolume = (1\/3) 3.5 x 1.25<br \/>\nvolume = (4.375\/3)<br \/>\nvolume =1.458 cu. in<\/p>\n<p><strong>10.6 Cross Sections of Three-Dimensional Figures (pp. 439\u2013444)<\/strong><br \/>\nLearning Target: Describe the cross sections of a solid.<\/p>\n<p>Describe the intersection of the plane and the solid.<br \/>\nQuestion 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27665\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-28.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 28\" width=\"132\" height=\"104\" \/><br \/>\nAnswer:<br \/>\nThe intersection of the plane of the solid = two dimensional<br \/>\nThe\u00a0 cross section of a solid = rectangular prism<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27666\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume-cr-29.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume cr 29\" width=\"126\" height=\"110\" \/><br \/>\nAnswer:<br \/>\nThe intersection of the plane of the solid = two dimensional<br \/>\nThe\u00a0 cross section of a solid = triangular prism<\/p>\n<p>Sketch how a plane can intersect with a cylinder to form a cross section of the given shape.<br \/>\nQuestion 27.<br \/>\nrectangle<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34165\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-10.png\" alt=\"\" width=\"268\" height=\"231\" \/><\/p>\n<p>Question 28.<br \/>\ncircle<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34167\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-11-300x231.png\" alt=\"\" width=\"300\" height=\"231\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-11-300x231.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-7-chapter-7.2-lesson-10-11.png 324w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 29.<br \/>\nline segment<br \/>\nAnswer:<\/p>\n<h3><a id=\"Surface_Area_and_Volume_Practice_Test\"><\/a>Surface Area and Volume Practice Test<\/h3>\n<p><strong>Find the surface area of the prism or regular pyramid.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27676\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-pt-1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume pt 1\" width=\"148\" height=\"84\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the pyramid = 7 ft<\/p>\n<p>Explanation:<br \/>\nThe surface area of the pyramid = (1\/3) x B h<br \/>\nsurface area = (1\/3) X 7 x 3<br \/>\nsurface area = (21\/3)<br \/>\nsurface area = 7 sq. ft<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27677\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-pt-2.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume pt 2\" width=\"85\" height=\"109\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the pyramid = 0.66 sq. in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the pyramid = (1\/3) x B h<br \/>\nsurface area = (1\/3) X 1 x 2<br \/>\nsurface area = (2\/3)<br \/>\nsurface area = 0.66 sq. in<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27678\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-pt-3.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume pt 3\" width=\"112\" height=\"114\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the pyramid = 47.5 sq. m<\/p>\n<p>Explanation:<br \/>\nThe surface area of the pyramid = (1\/3) x B h<br \/>\nsurface area = (1\/3) X 9.5 x 15<br \/>\nsurface area = (142.5\/3)<br \/>\nsurface area = 47.5 sq. m<\/p>\n<p>Find the surface area and lateral surface area of the cylinder. Round your answers to the nearest tenth.<br \/>\nQuestion 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27679\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-pt-4.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume pt 4\" width=\"137\" height=\"114\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the cylinder = 62.8 sq. cm<br \/>\nThe lateral surface area of the cylinder = 37.68 sq. cm<\/p>\n<p>Explanation:<\/p>\n<p>The surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere\u00a0 radius = 2 , height = 3 given<br \/>\nsurface area = 2 x 3.14 x 2 x 2 + 2 x 3.14 x 2 x 3<br \/>\nsurface area =\u00a0 25.12+ 37.68<br \/>\nsurface area = 62.8 sq. cm<br \/>\nThe lateral surface area of the cylinder =\u00a0 2\u03c0rh<br \/>\nwhere\u00a0 radius = 2\u00a0 , height = 3 given<br \/>\nsurface area =\u00a0 2 x 3.14 x 2 x 3<br \/>\nsurface area = 37.68 sq. cm<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27680\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-pt-5.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume pt 5\" width=\"152\" height=\"140\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the cylinder = 1623.38 sq. in<br \/>\nThe lateral surface area of the cylinder = 863.5 sq. in<\/p>\n<p>Explanation:<br \/>\nThe surface area of the cylinder = 2\u03c0r<sup>2<\/sup> + 2\u03c0rh<br \/>\nwhere\u00a0 radius = 11 , height = 12.5 given<br \/>\nsurface area = 2 x 3.14 x 11 x 11 + 2 x 3.14 x 11 x 12.5<br \/>\nsurface area =\u00a0 759.88+ 863.5<br \/>\nsurface area = 1623.38 sq. in<br \/>\nThe lateral surface area of the cylinder =\u00a0 2\u03c0rh<br \/>\nwhere\u00a0 radius = 11\u00a0 , height = 12.5 given<br \/>\nsurface area =\u00a0 2 x 3.14 x 11 x 12.5<br \/>\nsurface area = 863.5 sq. in<\/p>\n<p><strong>Find the volume of the solid.<\/strong><br \/>\nQuestion 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27681\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-pt-6.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume pt 6\" width=\"151\" height=\"95\" \/><br \/>\nAnswer:<br \/>\nVolume of the prism = 324 cu. in<\/p>\n<p>Explanation:<br \/>\nVolume of the prism =( bhl\/2)<br \/>\nvolume = (9 x `12 x 6\/2)<br \/>\nvolume =(648 \/2)<br \/>\nvolume = 324 cu. in<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27682\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-pt-7.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume pt 7\" width=\"142\" height=\"141\" \/><br \/>\nAnswer:<br \/>\nVolume of the prism = 41.6 cu. yd<\/p>\n<p>Explanation<br \/>\nVolume of the prism =lwh<br \/>\nvolume = (4 x `2 x 5.2)<br \/>\nvolume =(41.6)<br \/>\nQuestion 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27683\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-pt-8.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume pt 8\" width=\"135\" height=\"104\" \/><br \/>\nAnswer:<br \/>\nVolume of the prism = 72 cu. m<\/p>\n<p>Explanation:<br \/>\nVolume of the prism =( bhl\/2)<br \/>\nvolume = (3 x `8 x 6\/2)<br \/>\nvolume =(144\/2)<br \/>\nvolume = 72 cu. m<\/p>\n<p>Question 9.<br \/>\nA quart of paint covers 80 square feet. How many quarts should you buy to paint the ramp with two coats? (Assume you will not paint the bottom of the ramp.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27684\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-pt-9.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume pt 9\" width=\"189\" height=\"85\" \/><br \/>\nAnswer:<br \/>\nVolume of the prism = 2914.8 cu. ft<\/p>\n<p>Explanation:<br \/>\nVolume of the prism =lwh<br \/>\nvolume = (14x 34.7 x 6)<br \/>\nvolume =2914.8 cu. ft<\/p>\n<p>Question 10.<br \/>\nA manufacturer wants to double the volume of the graham cracker box. The manufacturer will either double the height or double the width.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27685\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-pt-10.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume pt 10\" width=\"158\" height=\"159\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-pt-10.png 158w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-pt-10-150x150.png 150w\" sizes=\"(max-width: 158px) 100vw, 158px\" \/><br \/>\na. What is the volume of the new graham cracker box?<br \/>\nb. Which option uses less cardboard? Justify your answer.<br \/>\nc. A graham cracker takes up about 1.5 cubic inches of space. Write an inequality that represents the numbers of graham crackers that can \ufb01t in the new box.<br \/>\nAnswer:<br \/>\na. the volume of the new graham cracker box = 108 cu. in<\/p>\n<p>Explanation:<br \/>\nVolume of the prism =lwh<br \/>\nvolume = (9 x 2 x 6)<br \/>\nvolume = 108 cu. in<\/p>\n<p>Question 11.<br \/>\nThe label on the can of soup covers about 354.2 square centimeters. What is the height of the can? Round your answer to the nearest whole number.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27686\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-pt-11.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume pt 11\" width=\"121\" height=\"150\" \/><br \/>\nAnswer:<br \/>\nThe height of the can = 10,454.5672 cm<\/p>\n<p>Explanation:<br \/>\nThe lateral surface area of the cylinder =\u00a0 2\u03c0rh<br \/>\nwhere\u00a0 radius = 4.7 , height = 354.2 given<br \/>\nsurface area =\u00a0 2 x 3.14 x 4.7 x 354.2<br \/>\nsurface area = 10,454.5672 cm<\/p>\n<p>Question 12.<br \/>\nA lumberjack splits the cylindrical log from top to bottom with an ax, dividing it in half. Describe the shape that is formed by the cut.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27687\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-pt-12.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume pt 12\" width=\"49\" height=\"70\" \/><br \/>\nAnswer:<br \/>\ncylinder.<\/p>\n<p>Explanation:<br \/>\nThe shape that formed by the cut = cylinder<\/p>\n<h3><a id=\"Surface_Area_and_Volume_Cumulative_Practice\"><\/a>Surface Area and Volume Cumulative Practice<\/h3>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-27667\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-cp-1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume cp 1\" width=\"311\" height=\"348\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-cp-1.png 311w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-cp-1-268x300.png 268w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><br \/>\nQuestion 1.<br \/>\nA gift box and its dimensions are shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27668\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-cp-2.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume cp 2\" width=\"290\" height=\"111\" \/><br \/>\nWhat is the least amount of wrapping paper that you need to wrap the box?<br \/>\nA. 20 in.<sup>2<\/sup><br \/>\nB. 56 in.<sup>2<\/sup><br \/>\nC. 64 in.<sup>2<\/sup><br \/>\nD. 112 in.<sup>2<\/sup><br \/>\nAnswer:<br \/>\noption C is correct.<\/p>\n<p>Explanation:<br \/>\nThe least amount of wrapping paper that need to wrap the box = l x w x h<br \/>\n8 x 4 x 2<br \/>\n64<br \/>\nQuestion 2.<br \/>\nJames is getting ready for wrestling season. As part of his preparation, he plans to lose 5% of his body weight. James currently weighs 160 pounds. How much will he weigh, in pounds, after he loses 5% of his weight?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27669\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-cp-3.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume cp 3\" width=\"71\" height=\"63\" \/><br \/>\nAnswer:<br \/>\nhe weigh after he loses 5 % = 128<\/p>\n<p>Question 3.<br \/>\nHow far will the tip of the hour hand of the clock travel in 2 hours? (Use \\(\\frac{22}{7}\\) for \u03c0.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27670\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-cp-4.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume cp 4\" width=\"221\" height=\"232\" \/><br \/>\nF. 44 mm<br \/>\nG. 88 mm<br \/>\nH. 264 mm<br \/>\nI. 528 mm<br \/>\nAnswer:<br \/>\noption G is correct<\/p>\n<p>Explanation:<br \/>\nThe circumference of circle = 2 \u03c0 r h<\/p>\n<p>Question 4.<br \/>\nWhich value of x makes the equation true?<br \/>\n5x &#8211; 3 = 11<br \/>\nA. 1.6<br \/>\nB. 2.8<br \/>\nC. 40<br \/>\nD. 70<br \/>\nAnswer:<br \/>\noption B is correct<\/p>\n<p>Explanation:<br \/>\n5x &#8211; 3 = 11<br \/>\n5x = 11 + 3<br \/>\n5x = 14<br \/>\nx = (14\/3)<br \/>\nx = 2.8<br \/>\nQuestion 5.<br \/>\nA hockey rink contains 5 face-off circles. Each of these circles has a radius of 15 feet. What is the total area of all the face-off circles? (Use 3.14 for \u03c0.)<br \/>\nF. 706.5 ft <sup>2<\/sup><br \/>\nG. 2826 ft<sup>2<\/sup><br \/>\nH. 3532.5 ft<sup>2<\/sup><br \/>\nI. 14,130 ft<sup>2<\/sup><br \/>\nAnswer:<br \/>\nOption G is correct<\/p>\n<p>Explanation:<br \/>\nThe surface area of circle = 2rh\u03c0<br \/>\ncircle = 2 x 15 x 5 x 3.14<\/p>\n<p>Question 6.<br \/>\nHow much material is needed to make the popcorn container?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27671\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-cp-5.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume cp 5\" width=\"196\" height=\"166\" \/><br \/>\nA. 76\u03c0 in.<sup>2<\/sup><br \/>\nB. 84\u03c0 in.<sup>2\u00a0 \u00a0 \u00a0 \u00a0<\/sup><br \/>\nC. 92\u03c0 in.<sup>2<\/sup><br \/>\nD. 108\u03c0 in.<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\nThe material needed to make the popcorn container = 76\u03c0 in.<sup>2<\/sup><\/p>\n<p>Explanation:<br \/>\nThe lateral surface area = 2\u03c0rh<br \/>\nsurface area = 2 x 9.5 x 4 \u03c0<br \/>\nsurface area = 76\u03c0 in.<sup>2<\/sup><\/p>\n<p>Question 7.<br \/>\nWhat is the surface area of the square pyramid?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27672\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-cp-6.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume cp 6\" width=\"185\" height=\"198\" \/><br \/>\nF. 24 in.<sup>2<\/sup><br \/>\nG. 96 in.<sup>2<\/sup><br \/>\nH. 132 in.<sup>2<\/sup><br \/>\nI. 228 in.<sup>2<\/sup><br \/>\nAnswer:<br \/>\nOption g is correct<\/p>\n<p>Explanation:<br \/>\nsurface area = 2 x l x h<br \/>\nsurface area = 2 x 8 x 6<br \/>\nsurface area = 96 square inches<\/p>\n<p>Question 8.<br \/>\nA rectangular prism and its dimensions are shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27673\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-cp-7.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume cp 7\" width=\"382\" height=\"159\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-cp-7.png 382w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-cp-7-300x125.png 300w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><br \/>\nWhat is the volume, in cubic inches, of a rectangular prism whose dimensions are three times greater?<br \/>\nAnswer:<br \/>\nThe volume of rectangular prism = 24 cu. in<\/p>\n<p>Explanation:<br \/>\nThe volume of rectangular prism l w h<br \/>\nvolume = 4 x 3 x 2<br \/>\nvolume = 24 cu. in<br \/>\nQuestion 9.<br \/>\nWhat is the value of x?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27674\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-cp-8.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume cp 8\" width=\"146\" height=\"140\" \/><br \/>\nA. 20<br \/>\nB. 43<br \/>\nC. 44<br \/>\nD. 65<br \/>\nAnswer:<br \/>\noption A\u00a0 is correct<\/p>\n<p>Explanation:<br \/>\n(2x + 4) = 46<br \/>\n2x = (46 &#8211; 4)<br \/>\n2x = 42<br \/>\nx = 21<\/p>\n<p>Question 10.<br \/>\nWhich of the following are possible angle measures of a triangle?<br \/>\nF. 60\u00b0, 50\u00b0, 20\u00b0<br \/>\nG. 40\u00b0, 80\u00b0, 90\u00b0<br \/>\nH. 30\u00b0, 60\u00b0, 90\u00b0<br \/>\nI. 0\u00b0, 90\u00b0, 90\u00b0<br \/>\nAnswer:<br \/>\noption H is the correct<\/p>\n<p>Explanation:<br \/>\nThe angles of a triangle = 30\u00b0, 60\u00b0, 90\u00b0<\/p>\n<p>Question 11.<br \/>\nThe table shows the costs of buying matinee movie tickets.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-27675\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-cp-9.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 10 Surface Area and Volume cp 9\" width=\"497\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-cp-9.png 497w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-10-Surface-Area-and-Volume-cp-9-300x52.png 300w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><br \/>\nPart A Graph the data.<br \/>\nPart B Find and interpret the constant of proportionality for the graph of the line.<br \/>\nPart C How much does it cost to buy 8 matinee movie tickets?<br \/>\nAnswer:<\/p>\n<h5>Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume<\/h5>\n<p>Here you are at the end of the page. You have learned about formula solving and many other things that have helped you to solve the problems at the next level. If you come across some problems of a higher level then this site helps you to attempt those topics and even solve some. If in the future you want to refer by starting from trash, take a look at this site and clear all your doubts. Bookmark the site for future use and reach us whenever needed.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Surface Area and Volume is an important concept to learn and score good marks. Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume pdf is here. Follow the detailed explanation of BIM Grade 7 Chapter 10 Surface Area and Volume and maximize your score. Get the detailed and explanatory concept and preparatory &#8230; <a title=\"Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-7-chapter-10\/\" aria-label=\"More on Big Ideas Math Answers Grade 7 Chapter 10 Surface Area and Volume\">Read more<\/a><\/p>\n","protected":false},"author":12,"featured_media":89748,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/04\/Big-Ideas-Math-Answers-Grade-7-Chapter-10-Surface-Area-and-Volume.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/27449"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=27449"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/27449\/revisions"}],"predecessor-version":[{"id":90238,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/27449\/revisions\/90238"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89748"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=27449"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=27449"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=27449"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}