{"id":30601,"date":"2022-04-04T15:34:50","date_gmt":"2022-04-04T10:04:50","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=30601"},"modified":"2022-04-07T11:29:57","modified_gmt":"2022-04-07T05:59:57","slug":"big-ideas-math-answers-grade-8-chapter-10","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-8-chapter-10\/","title":{"rendered":"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids"},"content":{"rendered":"<p>Big Ideas Math Answers 8th Grade Ch 10 Volume and Similar Solids helps you to have strong fundamentals of concepts underlying. Learn the associated lessons of Volume and Similar Solids easily and quickly taking the help of the BIM Book Grade 8 Chapter 10 Answers. All the <strong>Big Ideas Math Grade 8 Answers<\/strong> Chapter 10 Concepts are sequenced as per the BIM Textbooks. Resolve all your queries taking the help of the Step by Step Solutions provided for Big Ideas Math 8th Grade Questions and attempt the exam with utmost confidence.<\/p>\n<h2>Big Ideas Math Book 8th Grade Answer Key Chapter 10 Volume and Similar Solids<\/h2>\n<p>Big Ideas Math Book Grade 8 Answer Key Chapter 10 Volume and Similar Solids is given by subject experts after extensive research and meets the Common Core State Standards Curriculum. Refer to the below links available for BIM Textbook 8th Grade Ch 10 Volume and Similar Solids Solution Key and clear all your concerns in no time. Download the Volume and Similar Solids Big Ideas Math 8th Grade Answers for free of cost.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Volume_and_Similar_Solids_STEAM_Video\/Performance_Task\">Volume and Similar Solids STEAM Video\/Performance Task<\/a><\/li>\n<li><a href=\"#Volume_and_Similar_Solids_Getting_Ready_for_Chapter_10\">Volume and Similar Solids Getting Ready for Chapter 10<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 1 Volumes of Cylinders<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.1_Volumes_of_Cylinders\">Lesson 10.1 Volumes of Cylinders<\/a><\/li>\n<li><a href=\"#Volumes_of_Cylinders_Homework_&amp;_Practice_10.1\">Volumes of Cylinders Homework &amp; Practice 10.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Volumes of Cones<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.2_Volumes_of_Cones\">Lesson 10.2 Volumes of Cones<\/a><\/li>\n<li><a href=\"#Volumes_of_Cones_Homework_&amp;_Practice_10.2\">Volumes of Cones Homework &amp; Practice 10.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Volumes of Spheres<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.3_Volumes_of_Spheres\">Lesson 10.3 Volumes of Spheres<\/a><\/li>\n<li><a href=\"#Volumes_of_Spheres_Homework_&amp;_Practice_10.3\">Volumes of Spheres Homework &amp; Practice 10.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Surface Areas and Volumes of Similar Solids<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_10.4_Surface_Areas_and_Volumes_of_Similar_Solids\">Lesson 10.4 Surface Areas and Volumes of Similar Solids<\/a><\/li>\n<li><a href=\"#Surface_Areas_and_Volumes_of_Similar_Solids_Homework_&amp;_Practice_10.4\">Surface Areas and Volumes of Similar Solids Homework &amp; Practice 10.4<\/a><\/li>\n<\/ul>\n<p><strong>Chapter: 10 &#8211; Volume and Similar Solids<\/strong><\/p>\n<ul>\n<li><a href=\"#Volume_and_Similar_Solids_Connecting_Concepts\">Volume and Similar Solids Connecting Concepts<\/a><\/li>\n<li><a href=\"#Volume_and_Similar_Solids_Chapter_Review\">Volume and Similar Solids Chapter Review<\/a><\/li>\n<li><a href=\"#Volume_and_Similar_Solids_Practice_Test\">Volume and Similar Solids Practice Test<\/a><\/li>\n<li><a href=\"#Volume_and_Similar_Solids_Cumulative_Practice\">Volume and Similar Solids Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Volume_and_Similar_Solids_STEAM_Video\/Performance_Task\"><\/a>Volume and Similar Solids STEAM Video\/Performance Task<\/h3>\n<p><strong>STEAM Video<\/strong><\/p>\n<p>Canning Salsa<br \/>\nYou can estimate the volumes of ingredients to predict the total volume of a finished recipe. In what other real-life situations is it helpful to know the volumes of objects?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30645\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 1\" width=\"199\" height=\"305\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-1.png 199w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-1-196x300.png 196w\" sizes=\"(max-width: 199px) 100vw, 199px\" \/><br \/>\nWatch the STEAM Video \u201cCanning Salsa.\u201d Then answer the following questions.<br \/>\n1. You can approximate the volumes of foods by comparing them to common solids. A cube of cheese has side lengths of 3 centimeters. What is the volume of the cheese?<br \/>\n2. The table shows the amounts x (in cubic inches) of tomato used to make y cubic inches of salsa.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30646\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-2.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 2\" width=\"295\" height=\"70\" \/><br \/>\na. Is there a proportional relationship between x and y? Justify your answer.<br \/>\nb. How much tomato do you need to make 15 cubic inches of salsa?<\/p>\n<p>Answer:<br \/>\n1. The volume of the cheese = 27 cubic centimeters.<br \/>\n2. a = 1: 3 relationship.<br \/>\nb. 5 tomatoes are used to make 15 cubic inches of salsa.<\/p>\n<p>Explanation:<br \/>\n1. Given that a cube of cheese has a side length of 3 centimeters.<br \/>\nthe volume of cube = s\u00b3<br \/>\nvolume = side x side x side<br \/>\nvolume = 3 x 3 x 3<br \/>\nvolume = 27 cubic centimeters.<br \/>\n2. The relationship given in the above table is a 1: 3\u00a0 ratio.<br \/>\n1 x 3 = 3<br \/>\n2 x 3 = 6<br \/>\n3 x 3 = 9<br \/>\n4 x 3 = 12.<br \/>\nb. The tomatoes\u00a0 used to make 15 cubic inches of salsa = 5<br \/>\n5 x 3 = 15<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Packaging Salsa<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 jar and a shipping box.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30647\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-3.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 3\" width=\"612\" height=\"335\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-3.png 612w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-3-300x164.png 300w\" sizes=\"(max-width: 612px) 100vw, 612px\" \/><br \/>\nYou will be asked questions about how to package jars of salsa. Why is it helpful to know how many jars of salsa fit in one box?<\/p>\n<h3><a id=\"Volume_and_Similar_Solids_Getting_Ready_for_Chapter_10\"><\/a>Volume and Similar Solids Getting Ready for Chapter 10<\/h3>\n<p>Chapter Exploration<br \/>\n1. Work with a partner.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30648\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-4.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 4\" width=\"431\" height=\"317\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-4.png 431w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-4-300x221.png 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><br \/>\na. How does the volume of the stack of dimes compare to the volume of a single dime?<br \/>\nb. How does the volume of the stack of nickels compare to the volume of the stack of dimes? Explain your reasoning. (The height of each stack is identical.)<br \/>\nc. How does the volume of each stack change when you double the number of coins?<br \/>\nd. LOGIC Your friend adds coins to both stacks so that the volume of the stack of dimes is greater than the volume of the stack of nickels. What can you conclude about the number of coins added to each stack? Explain your reasoning.<\/p>\n<p><strong>Vocabulary<\/strong><\/p>\n<p>The following vocabulary terms are defined in this chapter. Think about what each term might mean and record your thoughts.<br \/>\ncone<br \/>\nhemisphere<br \/>\nsphere<br \/>\nsimilar solids<\/p>\n<p>Answer:<br \/>\ncone = A solid or hollow object which tapers from a circular or roughly circular base to a point.<br \/>\nhemisphere = a half of the celestial sphere as divided into two halves by the horizon.<br \/>\nsphere = a round solid figure, or its surface, with every point on its surface equidistant from its center.<br \/>\nsimilar solids = two solids are similar if they are the same type of solid and their corresponding radii, heights, base lengths, widths, etc. are proportional.<\/p>\n<h3><a id=\"Lesson_10.1_Volumes_of_Cylinders\"><\/a>Lesson 10.1 Volumes of Cylinders<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Exploring Volume<br \/>\nWork with a partner.<br \/>\na. Each prism shown has a height of h units and bases with areas of B square units. Write a formula that you can use to find the volume of each prism.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30649\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 1\" width=\"575\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-1.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-1-300x115.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><br \/>\nb. How can you find the volume of a prism with bases that each have 100 sides?<br \/>\nc. Make a conjecture about how to find the volume of a cylinder. Explain your reasoning.<\/p>\n<p>Answer:<br \/>\na. Volume of triangular prism = (bhl\/2)<br \/>\nrectangular prism = lwh<br \/>\npentagonal prism =(1\/2)(5 s x a) h<br \/>\nHexagonal prism = BH<br \/>\noctagonal prism = (A x H)\/2<br \/>\nb. volume of prism = 5,00,000<br \/>\nc. volume of cylinder = \u03c0r\u00b2 h<\/p>\n<p>Explanation:<br \/>\na. volume of traingular prism = (bhl\/2)<br \/>\nwhere b = base, h = height, l= length.<br \/>\nrectangular prism = lwh<br \/>\nwhere l = length, w= width, h= height.<br \/>\npentagonal prism = (1\/2) x (5 s x a) h<br \/>\nwhere s = side , a= area , h= height.<br \/>\nhexagonal prism = BH<br \/>\nwhere b = base h = height<br \/>\noctagonal prism = (A X H)\/2<br \/>\nA = area , H = height<br \/>\nvolume of triangular prism = (bhl\/2)<br \/>\nvolume = (100 x 100 x 100\/2)<br \/>\nvolume = (100x 100 x 50)<br \/>\nvolume = 5,00,000<br \/>\nvolume of cylinder =\u03c0r\u00b2 h<br \/>\nwhere r = radius and h = height.<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Finding Volume Experimentally<br \/>\nWork with a partner. Draw a net for a cylinder. Then cut out the net and use tape to form an open cylinder. Repeat this process to form an open cube. The edge length of the cube should be greater than the diameter and the height of the cylinder.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30650\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-2.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 2\" width=\"268\" height=\"222\" \/><br \/>\na.Use your conjecture in Exploration 1 to find the volume of the cylinder.<br \/>\nb. Fill the cylinder with rice. Then pour the rice into the open cube. Find the volume of rice in the cube. Does this support your answer in part(a)? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\na. volume of cylinder = \u03c0r\u00b2 h<br \/>\nb. we did not find the volume of rice in the cube.<\/p>\n<p>Explanation:<br \/>\na. volume of cylinder\u00a0 = \u03c0r\u00b2 h<br \/>\nwhere r = radius , h = height<br \/>\nb. we did not find the volume of rice in the cube because they did not give the value for the volume of rice.<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nFind the volume of a cylinder with a radius of 4 feet and a height of 15 feet. Round your answer to the nearest tenth.<\/p>\n<p>Answer:<br \/>\nvolume of cylinder = \u00a0753.6 cubic feet.<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder =\u03c0r\u00b2 h<br \/>\nwhere r = radius and h = height.<br \/>\nr = 4 feet , h = 15 feet \u03c0 = 3.14 given.<br \/>\nv = \u03c0 x 4 x 4 x 15<br \/>\nv = 3.14 x 16 x 15<br \/>\nv = 753.6 cubic feet.<\/p>\n<p>Question 2.<br \/>\nFind the height of the cylinder at the left. Round your answer to the nearest tenth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30651\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-3.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 3\" width=\"151\" height=\"133\" \/><\/p>\n<p>Answer:<br \/>\nheight of the cylinder =0.28545 cm<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder =\u03c0r\u00b2 h<br \/>\nwhere r = radius and h = height.<br \/>\nr = 4 cm , v = 176\u00a0 \u03c0 = 3.14 given.<br \/>\n176= \u03c0 x 4\u00a0 x 4 x h<br \/>\n176= 3.14 x 16 h<br \/>\n176 = 50.24 h<br \/>\nh = (50.24\/176)<br \/>\nh = 0.28545 cm<\/p>\n<p><strong>Find the radius 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-30652\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-4.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 4\" width=\"128\" height=\"144\" \/><\/p>\n<p>Answer:<br \/>\nradius of the cylinder = 0.2242 m\u00b2<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder =\u03c0r\u00b2 h<br \/>\nwhere r = radius and h = height.<br \/>\nh = 4 m , v = 28\u00a0 \u03c0 = 3.14 given.<br \/>\n28= \u03c0 x r\u00a0 x r x 4<br \/>\n28= 3.14 x 4 r\u00b2<br \/>\n28 = 12.56 r\u00b2<br \/>\nr\u00b2\u00a0= (12.56\/28)<br \/>\nr\u00b2 = 0.44857143 m\u2074<br \/>\nr = 0.2242 m\u00b2<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30653\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-5.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 5\" width=\"192\" height=\"128\" \/><\/p>\n<p>Answer:<br \/>\nradius of the cylinder =0.01183067 mm\u00b2<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder =\u03c0r\u00b2 h<br \/>\nwhere r = radius and h = height.<br \/>\nh = 4.25mm , v = 564\u00a0 \u03c0 = 3.14 given.<br \/>\n564= \u03c0 x r\u00a0 x r x 4.25<br \/>\n564= 3.14 x 4.25 r\u00b2<br \/>\n564= 13.345 r\u00b2<br \/>\nr\u00b2 = (13.345\/564)<br \/>\nr\u00b2 = 0.02366135.<br \/>\nr = 0.01183067 mm\u00b2<\/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>FINDING THE VOLUME OF A CYLINDER<\/strong><br \/>\nFind the volume of the cylinder at the left. Round your answer to the nearest tenth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30654\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-6.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 6\" width=\"150\" height=\"122\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cylinder = 43.96 cu yds<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 diameter = 4 given<br \/>\nso radius = (d\/2)<br \/>\nr = (4\/2)<br \/>\nr = 2 , h = 3.5<br \/>\nv = 3.14 x 2 x 2 x 3.5<br \/>\nv = 6.28 x 2 x 3.5<br \/>\nv = 12.56 x 3.5<br \/>\nv = 43.96 cu yds<\/p>\n<p>Question 6.<br \/>\n<strong>FINDING THE HEIGHT OF A CYLINDER<\/strong><br \/>\nFind the height of the cylinder at the right. Round your answer to the nearest tenth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30655\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 7\" width=\"165\" height=\"103\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cylinder = 43.96 cu yds<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 diameter = 4 given<br \/>\nso radius = (d\/2)<br \/>\nr = (4\/2)<br \/>\nr = 2 , h = 3.5<br \/>\nv = 3.14 x 2 x 2 x 3.5<br \/>\nv = 6.28 x 2 x 3.5<br \/>\nv = 12.56 x 3.5<br \/>\nv = 43.96 cu yds<\/p>\n<p>Question 7.<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-30656\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-8.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 8\" width=\"133\" height=\"145\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cylinder = 942 cu cm<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 r = 5 cm<br \/>\nr = 5 , h = 12 given<br \/>\nv = 3.14 x 5 x 5 x 12<br \/>\nv = 3.14 x 25 x 12<br \/>\nv = 78.5 x 12<br \/>\nv = 942 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 8.<br \/>\nHow much salsa is missing from the jar? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30657\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-9.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 9\" width=\"187\" height=\"180\" \/><\/p>\n<p>Answer:<br \/>\nThe salsa missing from the jar = 6 cm<\/p>\n<p>Explanation:<br \/>\nGiven that the jar height = 10 cm<br \/>\nsalsa filled is 4 cm<br \/>\nsalsa missing from the jar = 10 &#8211; 4<br \/>\nsalsa missing from the jar = 6 cm<\/p>\n<p>Question 9.<br \/>\nA cylindrical swimming pool has a circumference of 18\u03c0 feet and a height of 4 feet. About how many liters of water are needed to fill the swimming pool to 85% of its total volume? Justify your answer. (1 ft<sup>3<\/sup> \u2248 28.3 L)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30658\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-10.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 10\" width=\"186\" height=\"97\" \/><\/p>\n<p>Answer:<br \/>\nThe total amount of water needed to fill the swimming pool = 9 feet<\/p>\n<p>Explanation:<br \/>\nNo of liters of water = volume of cylinder = \u03c0r\u00b2 h<br \/>\nh = 4 feet given,<br \/>\ncircumference = 18 \u03c0 feet given<br \/>\n2 \u03c0r = 18 \u03c0<br \/>\n\u03c0 get canceled on both sides.<br \/>\n2r = 18<br \/>\nr = 9 feet<\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA company creates two designs for a cylindrical soup can. Can A has a diameter of 3.5 inches and a height of 3.6 inches. Can B has a height of 4.9 inches. Each can holds the same amount of soup. Which can requires less material to make? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\ncan B requires less material to make.<\/p>\n<p>Explanation:<br \/>\nvolume of the cylinder = \u03c0r\u00b2 h<br \/>\nvolume of can A = \u03c0r\u00b2 h<br \/>\nh = 3.6 in,diameter = 3.5 in given where r = (d\/2)<br \/>\nr = (3.5\/2) = 1.75 in<br \/>\nv = 3.14 x 1.75 x 1.75 x 3.6<br \/>\nv = 3.14 x 3.0625 x 3.6<br \/>\nv = 3.14 x 11.025<br \/>\nv = 34.6185 cu in<br \/>\nvolume of can B = \u03c0r\u00b2 h<br \/>\nh = 4.9 in,diameter = 3.5 in given where r = (d\/2)<br \/>\nr = (3.5\/2) = 1.75 in<br \/>\nv = 3.14 x 3.5 x 3.5 x 3.6<br \/>\nv = 3.14 x 12.25 x 3.6<br \/>\nv = 3.14 x 44.1<br \/>\nv = 138.474 cu in<\/p>\n<h3><a id=\"Volumes_of_Cylinders_Homework_&amp;_Practice_10.1\"><\/a>Volumes of Cylinders Homework &amp; Practice 10.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Tell whether the triangle with the given side lengths is a right triangle.<\/strong><br \/>\nQuestion 1.<br \/>\n20 m, 21 m, 29 m<\/p>\n<p>Answer:<br \/>\nYes, the given side lengths form a right triangle.<\/p>\n<p>Explanation:<br \/>\nThe length of any sides of right triangle = a\u00b2 + b\u00b2 = c\u00b2<br \/>\na\u00b2 + b\u00b2 = c\u00b2 = a\u00b2 + 2b= c\u00b2<br \/>\na = 20 , b = 21, c = 29<br \/>\n400 + 441 = 841<br \/>\n841 is equal to 841<\/p>\n<p>Question 2.<br \/>\n1 in., 2.4 in., 2.6 in.<\/p>\n<p>Answer:<br \/>\nthe given side lengths is not a right triangle.<\/p>\n<p>Explanation:<br \/>\nThe length of any sides of right triangle = a\u00b2 + b\u00b2 = c\u00b2<br \/>\na\u00b2 + b\u00b2 = c\u00b2 = a\u00b2 + 2b= c\u00b2<br \/>\na = 1 , b = 2.4, c = 2.6<br \/>\n1+ 2.4 x 2 = 6.76<br \/>\n5.8 = 6.76<br \/>\n5.8 is not equal to 6.76<\/p>\n<p>Question 3.<br \/>\n5.6 ft, 8 ft, 10.6 ft<\/p>\n<p>Answer:<br \/>\nthe given side lengths is not a right triangle.<\/p>\n<p>Explanation:<br \/>\nThe length of any sides of right triangle = a\u00b2 + b\u00b2 = c\u00b2<br \/>\na\u00b2 + b\u00b2 = c\u00b2 = a\u00b2 + 2b= c\u00b2<br \/>\na = 5.6 , b = 8, c = 10.6<br \/>\n5.6 x 5.6 + 8 x 2 = 10.6 x 10.6<br \/>\n31.36 + 16 = 112.36<br \/>\n47.36 = 112.36<br \/>\n47.36 is not equal to 112.36<\/p>\n<p><strong>Write the number in standard form.<\/strong><br \/>\nQuestion 4.<br \/>\n3.9 \u00d7 10<sup>6<\/sup><\/p>\n<p>Answer:<br \/>\n3.9000000<\/p>\n<p>Explanation:<br \/>\n3.9 x 10\u2076<br \/>\n3.9 x (10\u2075 x 10\u2076)<br \/>\n3.9 x (10 \u2075\u207a\u2076)<br \/>\nusing a\u1d50x a\u1d51 = a\u1d50\u207a\u1d51<br \/>\n3.9 x (10 \u00b9\u00b9)<br \/>\n3.9 x 10\u00b9\u00b9<br \/>\n3.900000000000<\/p>\n<p>Question 5.<br \/>\n6.7 \u00d7 10<sup>-5<\/sup><\/p>\n<p>Answer:<br \/>\n0.000067<\/p>\n<p>Explanation:<br \/>\n6.7x 10<sup>-5<br \/>\n6.7 x 10-\u2074 x 10-5<br \/>\n<\/sup>6.7 x (10<sup>-\u2074-\u00a0\u2075)<br \/>\n6.7 x 10-\u2079<br \/>\n0.000067<\/sup><\/p>\n<p>Question 6.<br \/>\n6.24 \u00d7 10<sup>10<\/sup><\/p>\n<p>Answer:<br \/>\n6.240000000000<\/p>\n<p>Explanation:<br \/>\n<sup>6.24 x 10\u00b9\u2070<br \/>\n6.24 x (10\u2079 x 10\u00b9\u2070)<br \/>\n6.24 x (10\u2079 \u207a\u00b9\u2070)<br \/>\nusing a\u1d50x a\u1d51 = a\u1d50\u207a\u1d51<br \/>\n6.24 x (10 \u00b9\u2079 )<br \/>\n6.24 x 10\u00b9\u2079<br \/>\n6.240000000000000000000<\/sup><\/p>\n<p>Question 7.<br \/>\nWhich ordered pair is the solution of the linear system 3x + 4y = -10 and 2x &#8211; 4y = 0?<br \/>\nA. (6, 2)<br \/>\nB. (2, 6)<br \/>\nC. (2, 1)<br \/>\nD. (1, 2)<\/p>\n<p>Answer:<br \/>\noption c is correct.<\/p>\n<p>Explanation:<br \/>\n3x + 4y = -10<br \/>\n3 (2) + 4 (1) = -10<br \/>\n6 + 4 = -10<br \/>\n2x &#8211; 4y = 0<br \/>\n2 (2) &#8211; 4 (1) = 0<br \/>\n4 &#8211; 4 = 0<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>FINDING VOLUME<\/strong> The height h and the base area B of a cylinder are given. Find the volume of the cylinder. Write your answer in terms of \u03c0. (See Explorations 1 and 2, p. 427.)<br \/>\nQuestion 8.<br \/>\nh = 5 units<br \/>\nB = 4\u03c0 square units<\/p>\n<p>Answer:<br \/>\nvolume of cylinder = 251.2 \u03c0 cubic units<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 r = 4\u03c0<br \/>\nr = 4\u03c0 , h = 5 given<br \/>\nv = 3.14 x 4 x 4 x 5<br \/>\nv = 3.14 x 16 x 5<br \/>\nv = 251.2<br \/>\nv = 251.2 \u03c0 cubic\u00a0 units<\/p>\n<p>Question 9.<br \/>\nh = 2 units<br \/>\nB = 25\u03c0 square units<\/p>\n<p>Answer:<br \/>\nvolume of cylinder = 50 \u03c0 cubic units<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 r = 25\u03c0<br \/>\nr = 25\u03c0 , h = 2 given<br \/>\nv = 3.14 x 25x 25 x 2<br \/>\nv = 3.14 x 25 x 2<br \/>\nv = 3.14 x 50<br \/>\nv = 50 \u03c0 cu. units<\/p>\n<p>Question 10.<br \/>\nh = 4.5 units<br \/>\nB = 16\u03c0 square units<\/p>\n<p>Answer:<br \/>\nvolume of cylinder = 3,617.28 \u03c0 cu. units<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 r = 16\u03c0<br \/>\nr = 16\u03c0 , h = 4.5 given<br \/>\nv = 3.14 x 16 x 16 x 4.5<br \/>\nv = 3.14 x 256 x 4.5<br \/>\nv = 3.14 x 1152<br \/>\nv = 3,617.28\u00a0 \u03c0 cu. units<\/p>\n<p><strong>FINDING THE VOLUME OF A CYLINDER<\/strong> Find the volume of the cylinder. Round your answer to the nearest tenth.<br \/>\nQuestion 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30659\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 11\" width=\"144\" height=\"88\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cylinder = 1,526.04 cu. feet<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 r = 9<br \/>\nr = 9 , h = 6 given<br \/>\nv = 3.14 x 9 x 9 x 6<br \/>\nv = 3.14 x 81 x 6<br \/>\nv = 3.14 x 486<br \/>\nv = 1,526.04 cu. feet<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30660\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-12.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 12\" width=\"117\" height=\"104\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cylinder = 791.28 cu. in<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 r = 6<br \/>\nr = 6 , h = 7 given<br \/>\nv = 3.14 x 6 x 6 x 7<br \/>\nv = 3.14 x 36 x 7<br \/>\nv = 3.14 x 252<br \/>\nv = 791.28 cu. in<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30661\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-13.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 13\" width=\"156\" height=\"104\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cylinder = 769.3 cu feet<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 r = 7<br \/>\nr = 7 , h = 5 given<br \/>\nv = 3.14 x 7 x 7 x 5<br \/>\nv = 3.14 x 49 x 5<br \/>\nv = 3.14 x 245<br \/>\nv = 769.3 cu feet<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30662\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-14.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 14\" width=\"142\" height=\"156\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cylinder = 785 cu. feet<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 r = 5 ft<br \/>\nr = 5 , h = 10 given<br \/>\nv = 3.14 x 5 x 5 x 10<br \/>\nv = 3.14 x 25 x 10<br \/>\nv = 3.14 x 250<br \/>\nv = 785 cu. feet<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30663\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-15.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 15\" width=\"166\" height=\"108\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cylinder = 804.2 cu. cm<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 r = 8 cm<br \/>\nr = 8 , h = 16 given<br \/>\nv = 3.14 x 8 x 8 x 16<br \/>\nv = 3.14 x 64 x 16<br \/>\nv = 3.14 x 1,024<br \/>\nv = 804.2 cu. cm<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30664\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-16.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 16\" width=\"160\" height=\"89\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cylinder = 883.125 cu. m<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 d = 15 r = (d\/2)<br \/>\nr = 7.5 , h = 5 given<br \/>\nv = 3.14 x 7.5 x 7.5 x 5<br \/>\nv = 3.14 x 56.25 x 5<br \/>\nv = 3.14 x 281.25<br \/>\nv = 883.125 cu. m<\/p>\n<p>Question 17.<br \/>\n<strong>REASONING<\/strong><br \/>\nWithout calculating, which of the solids has the greater volume? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30665\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-17.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 17\" width=\"301\" height=\"149\" \/><\/p>\n<p>Answer:<br \/>\nthe cube has a greater volume.<\/p>\n<p>Explanation:<br \/>\nthe volume of square prism = s\u00b3<br \/>\nv = side x side x side<br \/>\nv = 8 x 8 x 8<br \/>\nv = 64 x 8<br \/>\nv = 512 cubic inches<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 r = 4 cm<br \/>\nr = 4 , h = 8 given<br \/>\nv = 3.14 x 4 x 4 x 8<br \/>\nv = 3.14 x 16 x 8<br \/>\nv = 3.14 x 128<br \/>\nv = 401.92 cu. in<\/p>\n<p><strong>FINDING A MISSING DIMENSION<\/strong> Find the missing dimension of the cylinder. Round your answer to the nearest whole number.<br \/>\nQuestion 18.<br \/>\nVolume = 10,000 \u03c0 in.<sup>3<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30666\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-18.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 18\" width=\"177\" height=\"105\" \/><\/p>\n<p>Answer:<br \/>\nheight of cylinder = 0.080384 in<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 d = 32 r = (d\/2)<br \/>\nr = 16 , v = 10,000<br \/>\n10,000 = 3.14 x 16 x 16 x h<br \/>\n10,000 = 3.14 x 256 h<br \/>\n10,000= 803.84\u00a0 h<br \/>\nh = (803.84\/10,000)<br \/>\nh = 0.080384 in<\/p>\n<p>Question 19.<br \/>\nVolume = 3785 cm<sup>3<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30667\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-19.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 19\" width=\"160\" height=\"142\" \/><\/p>\n<p>Answer:<br \/>\nradius of cylinder = 8 cm<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 h = 19<br \/>\nv = 3785<br \/>\n3785 = 3.14 x r x r x 19<br \/>\n3785 = 3.14 x 19r\u00b2<br \/>\n3785= 59.66 r\u00b2<br \/>\nr\u00b2 = (3785\/59.66)<br \/>\nr\u00b2 =64<br \/>\nr = 8 cm<\/p>\n<p>Question 20.<br \/>\nVolume = 600,000 cm<sup>3<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30668\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-20.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 20\" width=\"184\" height=\"128\" \/><\/p>\n<p>Answer:<br \/>\nRadius of cylinder = 0.00198867 cm<\/p>\n<p>Explanation:<br \/>\nVolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 h = 76 cm given<br \/>\n, v = 600,000<br \/>\n600,000 = 3.14 x r x r x 76<br \/>\n600,000 = 3.14 x 76r\u00b2<br \/>\n600,000= 238.64r\u00b2<br \/>\nr\u00b2 = (238.64\/600,000)<br \/>\nr\u00b2 = 0.00397733<br \/>\nr = 0.00198867 cm<\/p>\n<p>Question 21.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA cylindrical hazardous waste container has a diameter of 1.5 feet and a height of 1.6 feet. About how many gallons of hazardous waste can the container hold? (1 ft<sup>3<\/sup> \u2248 7.5 gal)<\/p>\n<p>Answer:<br \/>\nHazardous waste can hold the container = 21.195 gal<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 d = 1.5 r = (d\/2)<br \/>\nr = 0.75 , h = 1.6 feet<br \/>\nv = 3.14 x 0.75 x 0.75 x 1.6<br \/>\nv = 3.14 x 0.5625 x 1.6<br \/>\nv= 3.14 x 0.9<br \/>\nh = 2.826<br \/>\nh = 2.826 x 7.5<br \/>\nh = 21.195 gal<\/p>\n<p>Question 22.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nHow does the volume of a cylinder change when its diameter is halved? Explain.<\/p>\n<p>Answer:<br \/>\nthe volume of the cylinder change when its diameter is halved.<\/p>\n<p>Explanation:<br \/>\nIf the diameter is halved it is the same as a radius.<br \/>\nd = (r\/2)<br \/>\n(d\/2)<br \/>\nso the volume of the cylinder change when its diameter is halved.<\/p>\n<p>Question 23.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA traditional \u201csquare\u201d bale of hay is actually in the shape of a rectangular prism. Its dimensions are 2 feet by 2 feet by4 feet. How many square bales contain the same amount of hay as one large \u201cround\u201d bale?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30669\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-21.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 21\" width=\"225\" height=\"200\" \/><\/p>\n<p>Answer:<br \/>\nThe square bales contain the same amount of hay as one large round bale = 4 squares bale<\/p>\n<p>Explanation:<br \/>\nThe surface area of rectangular prism = 2(lw + lh +wh)<br \/>\ngiven that l = 2, w=2 h = 4<br \/>\narea = 2(2 x 2 + 2 x 4 +4 x 2)<br \/>\narea = 2(4 + 8 + 8)<br \/>\narea = 2(2)<br \/>\narea = 4 sq ft<\/p>\n<p>Question 24.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA tank on a road roller is filled with water to make the roller heavy. The tank is a cylinder that has a height of 6 feet and a radius of 2 feet. About how many pounds of water can the tank hold? (One cubic foot of water weighs about 62.5 pounds.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30670\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-22.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 22\" width=\"193\" height=\"133\" \/><\/p>\n<p>Answer:<br \/>\nThe pounds of water can hold the tank = 4,710 pounds<\/p>\n<p>Explanation:<br \/>\nVolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 h = 6 ft given<br \/>\nr = 2 ft<br \/>\nv = 3.14 x 2 x 2 x 6<br \/>\nv = 3.14 x 4 x 6<br \/>\nv= 3.14 x 24<br \/>\nv = 75.36 cu. feet<br \/>\nv = 75.36 x 62.5<br \/>\nv = 4,710 pounds<\/p>\n<p>Question 25.<br \/>\n<strong>REASONING<\/strong><br \/>\nA cylinder has a surface area of 1850 square meters and a radius of 9 meters. Estimate the volume of the cylinder to the nearest whole number.<\/p>\n<p>Answer:<br \/>\nVolume of the cylinder = 6035 cubic meters.<\/p>\n<p>Explanation:<br \/>\nvolume of the cylinder= \u03c0r\u00b2h<br \/>\nvolume = 3.14 x 9 x 9 x 1850<br \/>\nvolume = 8325 &#8211; 729 \u03c0<br \/>\nv = 8325 &#8211; 729 x 3.14<br \/>\nv = 8325 &#8211; 102.06<br \/>\nv = 8222.94<br \/>\nthe nearest whole number to the 8222.94 is 6035 cubic meters.<\/p>\n<p>Question 26.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWater flows at 2 feet per second through a cylindrical pipe with a diameter of 8 inches. A cylindrical tank with a diameter of 15 feet and a height of 6 feet collects the water.<br \/>\na. What is the volume (in cubic inches) of water flowing out of the pipe every second?<br \/>\nb. What is the height (in inches) of the water in the tank after 5 minutes?<br \/>\nc. How many minutes will it take to fill 75% of the tank?<\/p>\n<p>Answer:<br \/>\na. Volume of water flowing out of the pipe every second = 100.48 cu. in<br \/>\nb. The height of the water in tank after 5 minutes = 1,059.75 sq ft<br \/>\nc. 75% of water to fill tank = 25<\/p>\n<p>Explanation:<br \/>\na. Volume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 h = 2 ft given<br \/>\nr = 4<br \/>\nv = 3.14 x 4 x 4 x 2<br \/>\nv = 3.14 x 16 x 2<br \/>\nv= 3.14 x 32<br \/>\nv = 100.48 cu. in<br \/>\nb. Volume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 h = 6 ft given<br \/>\nr = 7.5<br \/>\nv = 3.14 x 7.5 x 7.5 x 6<br \/>\nv = 3.14 x 56.25 x 6<br \/>\nv= 3.14 x 337.5<br \/>\nv = 1,059.75 cu. ft<br \/>\nc. 100 &#8211; 75<br \/>\n25 %<\/p>\n<p>Question 27.<br \/>\n<strong>PROJECT<\/strong><br \/>\nYou want to make and sell three different sizes of cylindrical candles. You buy 1 cubic foot of candle wax for $20 to make 8 candles of each size.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30671\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.1-23.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids 10.1 23\" width=\"198\" height=\"233\" \/><br \/>\na. Design the candles. What are the dimensions of each size of candle?<br \/>\nb. You want to make a profit of $100. Decide on a price for each size of candle. Explain how you set your prices.<\/p>\n<p>Answer:<br \/>\na. The dimensions of each size of candle = 20cm<br \/>\nb. price for each size of candle = $ 30<\/p>\n<p>Explanation:<br \/>\n$ x 80 candles given<br \/>\n20 x 3 = 60<br \/>\neach candle has a dimension of 20 cm<br \/>\nb. price for each side = $ 30<\/p>\n<h3><a id=\"Lesson_10.2_Volumes_of_Cones\"><\/a>Lesson 10.2 Volumes of Cones<\/h3>\n<p>You already learned how the volume of a pyramid relates to the volume of a cone prism. In this exploration, you will discover how the volume of a relates to the volume of a cylinder.<br \/>\nA cone is a solid that has one circular base and one vertex.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30672\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-1.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 1\" width=\"242\" height=\"176\" \/><\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Finding a Formula Experimentally<br \/>\nWork with a partner.Use a paper cup that is shaped like a cone. Measure the height of the cup and the diameter of the circular base. Use these measurements to draw a net for a cylinder with the same base and height as the paper cup. Then cut out the net and use tape to form an open cylinder.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30673\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-2.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 2\" width=\"370\" height=\"206\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-2.png 370w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-2-300x167.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><br \/>\na. Find the volume of the cylinder.<br \/>\nb. Fill the paper cup with rice. Then pour the rice into the cylinder. Repeat this until the cylinder is full. How many cones does it take to fill the cylinder?<br \/>\nc. Use your result to write a formula for the volume of a cone.<br \/>\nd. Use your formula in part(c) to find the volume of the cone. How can you tell whether your answer is correct?<br \/>\ne. Do you think your formula for the volume of a cone oblique is also true for cones? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\na. volume of cylinder = \u03c0r\u00b2 h<br \/>\nb. 2 cones will take to fill the cylinder.<br \/>\nc. volume of cone = \u03c0r\u00b2( h\/3)<br \/>\nd. yes the answer is correct.<br \/>\ne. volume of cone oblique is true for cones.<\/p>\n<p>Explanation:<br \/>\na.volume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere r = radius , h= height<br \/>\nb. 2 cones = 1 cylinder<br \/>\nc. . volume of cone = \u03c0r\u00b2( h\/3)<br \/>\nwhere r = radius , h= height<br \/>\nd. Yes the answer is correct.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-30674\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-3.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 3\" width=\"183\" height=\"70\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nFind the volume of a cone with a radius of 6 centimeters and a height of 15 centimeters. Round your answer to the nearest tenth.<\/p>\n<p>Answer:<br \/>\nvolume of cone = 565.2 cu. cm<\/p>\n<p>Explanation:<br \/>\nvolume of cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 6 ,h=15<br \/>\nv = 3.14 x 6 x 6 x (15\/3)<br \/>\nv = 3.14 x 36 x 5<br \/>\nv=3.14 x 180<br \/>\nv= 565.2 cu. cm<\/p>\n<p>Question 2.<br \/>\nFind the height of the cone at the left. Round your answer to the nearest tenth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30675\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-4.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 4\" width=\"143\" height=\"145\" \/><\/p>\n<p>Answer:<br \/>\nheight of cone = 0.03270833 yd<\/p>\n<p>Explanation:<br \/>\nvolume of cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 15 ,v = 7200<br \/>\n7200 = 3.14 x 15 x 15 x (h\/3)<br \/>\n7200 = 3.14 x 15 x 5h<br \/>\n7200=3.14 x 75h<br \/>\n7200= 235.5 h<br \/>\nh = (235.5\/7200)<br \/>\nh = 0.03270833<\/p>\n<p><strong>Find the radius of the cone. Round your answer to the nearest whole number.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30676\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-5.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 5\" width=\"152\" height=\"147\" \/><\/p>\n<p>Answer:<br \/>\nradius of cone = 12.4887397 feet<\/p>\n<p>Explanation:<br \/>\nvolume of cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that h = 7 ,v = 183<br \/>\n183 = 3.14 x r x r x (7\/3)<br \/>\n183 = 3.14 x r\u00b2 x 2.33<br \/>\n183=3.14 x 2.33 r\u00b2<br \/>\n183= 7.32666 r\u00b2<br \/>\nr\u00b2 = (183\/7.32666)<br \/>\nr\u00b2\u00a0 = 24.97747<br \/>\nr=12.4887397 feet<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30678\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-6.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 6\" width=\"169\" height=\"129\" \/><\/p>\n<p>Answer:<br \/>\nradius of cone = 1.78594585 meter<\/p>\n<p>Explanation:<br \/>\nvolume of cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that h = 2.75 ,v = 46<br \/>\n46 = 3.14 x r x r x (2.75\/3)<br \/>\n46 = 3.14 x r\u00b2 x 0.9166<br \/>\n46 = 12.87833 r\u00b2<br \/>\nr\u00b2 = (46\/12.87833)<br \/>\nr\u00b2\u00a0 = 3.57189<br \/>\nr=1.78594585 meter<\/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>FINDING THE VOLUME OF A CONE<\/strong><br \/>\nFind the volume of a cone with a diameter of 10 yards and a height of 12 yards. Round your answer to the nearest tenth.<\/p>\n<p>Answer:<br \/>\nvolume of cone = 314 cu. yards.<\/p>\n<p>Explanation:<br \/>\nvolume of cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that d = 10 r=(d\/2) r = (10\/2) r = 5 ,h=12<br \/>\nv = 3.14 x 5 x 5 x (12\/3)<br \/>\nv = 3.14 x 25 x 4<br \/>\nv=3.14 x 100<br \/>\nv= 314 cu. yards<\/p>\n<p><strong>FINDING A MISSING DIMENSION OF A CONE<\/strong> Find the missing dimension of the cone. Round your answer to the nearest tenth.<br \/>\nQuestion 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30679\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-7.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 7\" width=\"184\" height=\"82\" \/><\/p>\n<p>Answer:<br \/>\nheight of cone = 66.6666 in<\/p>\n<p>Explanation:<br \/>\nvolume of cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 6 ,v = 2,512<br \/>\n2512 = 3.14 x 6 x 6 x (h\/3)<br \/>\n2512 = 3.14 x 6 x 2h<br \/>\n2512 =3.14 x 12h<br \/>\n2512= 37.68h<br \/>\nh = (2512\/37.68)<br \/>\nh = 66.6666 in<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30680\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-8.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 8\" width=\"134\" height=\"144\" \/><\/p>\n<p>Answer:<br \/>\nradius of cone = 25.12 centimeter<\/p>\n<p>Explanation:<br \/>\nvolume of cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that h = 5 ,v = 16.5<br \/>\n16.5 = 3.14 x r x r x (5\/3)<br \/>\n16.5 = 3.14 x r\u00b2 x 1.666<br \/>\n16.5 = 5.23333 r\u00b2<br \/>\nr\u00b2 = (16.5\/5.23333)<br \/>\nr\u00b2\u00a0 = 3.152868<br \/>\nr= 8\u03c0 centimeter<\/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 8.<br \/>\nA stalactite is a mineral formation that hangs from the ceiling of a cave. A cone-shaped stalactite has a height of 48 centimeters and a base circumference of 3.5\u03c0 centimeters. What is the volume of the stalactite?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30682\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-9.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 9\" width=\"174\" height=\"205\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cone = 615.44 cu. cm<\/p>\n<p>Explanation:<br \/>\nvolume of cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r =3.5 ,h=48<br \/>\nv = 3.14 x 3.5 x 3.5 x (48\/3)<br \/>\nv = 3.14 x 12.25 x 16<br \/>\nv=3.14 x 196<br \/>\nv= 615.44 cu. cm<\/p>\n<p>Question 9.<br \/>\nA store sells two cone-shaped funnels. What is the height of each funnel? (1 pt = 28.875 in.<sup>3<\/sup>)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30683\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-10.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 10\" width=\"296\" height=\"113\" \/><\/p>\n<p>Answer:<br \/>\nheight of ist funnel =2.72469922 in<br \/>\nheight of 2nd funnel = 3.06528662 in<\/p>\n<p>Explanation:<br \/>\nvolume of 1st cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r= (d\/2)r = (4.5\/2) r = 2.25 ,v = 0.5<br \/>\n0.5 = 3.14 x 2.25 x 2.25 x (h\/3)<br \/>\n0.5 = 3.14 x 5.0625 x (h\/3)<br \/>\n0.5 =3.14 x 1.6875h<br \/>\n0.5= 5.29875 h<br \/>\nh = (0.5\/5.29875)<br \/>\nh = 0.09436188<br \/>\nh = 0.09436188 x 28.875<br \/>\nh = 2.72469922<br \/>\nvolume of 2nd cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r= (d\/2)r = (6\/2) r=3 ,v = 1<br \/>\n1 = 3.14 x 3 x 3 x (h\/3)<br \/>\n1 = 3.14 x 3x h<br \/>\n1 =3.14 x 3h<br \/>\n1= 9.42 h<br \/>\nh = (1\/9.42)<br \/>\nh = 0.10615711 x 28.875<br \/>\nh = 3.0652866<\/p>\n<p>Question 10.<br \/>\nYou fill cone-shaped pastry bags with icing to a height of 1 foot and a diameter of 3.5 inches. You use about 1.35 cubic inches of icing per cupcake. About how many cupcakes can you decorate with 2 bags of icing?<\/p>\n<p>Answer:<br \/>\nCupcakes can decorate with 2 bags of icing = 6.410833 sq in<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r= (d\/2)r = (3.5\/2) r=1.75 ,h = 1<br \/>\nv = 3.14 x 1.75 x 1.75 x (1\/3)<br \/>\nv = 3.14 x 3.0625 x (1\/3)<br \/>\nv =3.14 x 3.0625 x 0.333<br \/>\nv= 3.14 x 1.0208333<br \/>\nv = 3.20541667 inches<br \/>\nfor 2 bags of icing = 6.4108333<\/p>\n<h3><a id=\"Volumes_of_Cones_Homework_&amp;_Practice_10.2\"><\/a>Volumes of Cones Homework &amp; Practice 10.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the volume 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-30684\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-11.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 11\" width=\"116\" height=\"136\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone = 65.94 cu. cm<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r=3 ,h = 7<br \/>\nv = 3.14 x 3 x 3 x (7\/3)<br \/>\nv = 3.14 x 9 x (7\/3)<br \/>\nv =3.14 x 9 x 2.33<br \/>\nv= 3.14 x 21<br \/>\nv = 65.94 cu. cm<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30685\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-12.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 12\" width=\"150\" height=\"138\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone = 16.7466 cu. ft<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r=2 ,h = 4<br \/>\nv = 3.14 x 2 x 2 x (4\/3)<br \/>\nv = 3.14 x 4 x (4\/3)<br \/>\nv =3.14 x 4 x 1.33<br \/>\nv= 3.14 x 5.333<br \/>\nv = 16.7466 cu. ft<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30688\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-13.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 13\" width=\"160\" height=\"84\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone = 523.333 cu. yds<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r=10 ,h = 5<br \/>\nv = 3.14 x 10 x 10 x (5\/3)<br \/>\nv = 3.14 x 100 x (5\/3)<br \/>\nv =3.14 x 100 x 1.666<br \/>\nv= 3.14 x 166.66<br \/>\nv = 523.333 cu. yds<\/p>\n<p><strong>Solve the equation.<\/strong><br \/>\nQuestion 4.<br \/>\nx<sup>3<\/sup> = 27<\/p>\n<p>Answer:<br \/>\nx = 3<\/p>\n<p>Explanation:<br \/>\nx\u00b3 = 27<br \/>\nx\u00b3 = 3\u00b3<br \/>\nwhen power are equal exponents must be equal.<br \/>\nx = 3<\/p>\n<p>Question 5.<br \/>\n&#8211; 6 = y<sup>3<\/sup> + 2<\/p>\n<p>Answer:<br \/>\ny = &#8211; 2<\/p>\n<p>Explanation:<br \/>\n-6 = y\u00b3 + 2<br \/>\ny\u00b3 = 2 + 6<br \/>\ny\u00b3 = 8<br \/>\ny\u00b3 = 2\u00b3<br \/>\ny = -2<\/p>\n<p>Question 6.<br \/>\n2h<sup>3<\/sup> &#8211; 33 = 95<\/p>\n<p>Answer:<br \/>\nh = 4<\/p>\n<p>Explanation:<br \/>\n2h\u00b3 &#8211; 33 = 95<br \/>\n2h\u00b3 = 95 + 33<br \/>\n2h\u00b3 = 128<br \/>\nh\u00b3 = (128\/2)<br \/>\nh\u00b3 = 64<br \/>\nh\u00b3 = 4\u00b3<br \/>\nh = 4<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>FINDING A VOLUME<\/strong> The height h and the base B area of a cone are given. Find the volume of the cone. Write your answer in terms of \u03c0. (See Exploration 1, p. 433.)<br \/>\nQuestion 7.<br \/>\nh = 6 units<br \/>\nB = 4\u03c0 square units<\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone = 8 \u03c0 cubic units<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r=4 ,h = 6<br \/>\nv = 3.14 x 4 x 4 x (6\/3)<br \/>\nv = 3.14 x 16 x (6\/3)<br \/>\nv =3.14 x 4 x 2<br \/>\nv= 8 x \u03c0<br \/>\nv = 25.12 cubic units<\/p>\n<p>Question 8.<br \/>\nh = 9 units<br \/>\nB = 5\u03c0 square units<\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone = 235.5 cubic units<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r=5 ,h = 9<br \/>\nv = 3.14 x 5 x 5 x (9\/3)<br \/>\nv = 3.14 x 25 x (9\/3)<br \/>\nv =3.14 x 25 x 3<br \/>\nv= 3.14 x 75<br \/>\nv = 235.5 cubic units<\/p>\n<p><strong>FINDING THE VOLUME OF A CONE<\/strong> Find the volume of the cone. Round your answer to the nearest tenth.<br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30689\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-14.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 14\" width=\"111\" height=\"106\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone = 16.7466 cu. in<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r=2 ,h = 4<br \/>\nv = 3.14 x 2 x 2 x (4\/3)<br \/>\nv = 3.14 x 4 x (4\/3)<br \/>\nv =3.14 x 4 x 1.33<br \/>\nv= 3.14 x 5.33<br \/>\nv = 16.7466 cu. in<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30690\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-15.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 15\" width=\"129\" height=\"101\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone = 28.26 cu. m<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r=(d\/2) (6\/2)=3 ,h = 3<br \/>\nv = 3.14 x 3 x 3 x (3\/3)<br \/>\nv = 3.14 x 9 x (3\/3)<br \/>\nv =3.14 x 9 x 1<br \/>\nv= 3.14 x 9<br \/>\nv = 28.26 cu. m<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30691\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-16.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 16\" width=\"118\" height=\"113\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone =261.66 cu. mm<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 5 ,h = 10<br \/>\nv = 3.14 x 5 x 5 x (10\/3)<br \/>\nv = 3.14 x 25 x (10\/3)<br \/>\nv =3.14 x 25 x 3.33<br \/>\nv= 3.14 x 83.333<br \/>\nv = 261.66 cu. mm<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30692\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-17.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 17\" width=\"125\" height=\"92\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone =2.093333 cu. ft<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 1 ,h = 2<br \/>\nv = 3.14 x 1 x 1 x (2\/3)<br \/>\nv = 3.14 x 1 x (2\/3)<br \/>\nv =3.14 x 1 x 0.6666<br \/>\nv= 3.14 x 0.666<br \/>\nv = 2.093333 cu. ft<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30693\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-18.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 18\" width=\"131\" height=\"116\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone = 804.2 cubic cm<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 5 ,h = 8<br \/>\nv = 3.14 x 5 x 5 x (8\/3)<br \/>\nv = 3.14 x 25 x (8\/3)<br \/>\nv =3.14 x 25 x 2.6666<br \/>\nv= 3.14 x 256<br \/>\nv = 804.2 cubic cm<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30694\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-19.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 19\" width=\"160\" height=\"98\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone = 115.395 cu. yd<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r =(d\/2) = (7\/2) = 3. 5 ,h = 9<br \/>\nv = 3.14 x 3.5 x 3.5 x (9\/3)<br \/>\nv = 3.14 x 12.25 x (9\/3)<br \/>\nv =3.14 x 12.25 x 3<br \/>\nv= 3.14 x 36.75<br \/>\nv = 115.395 cu. yd<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30695\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-20.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 20\" width=\"131\" height=\"93\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone =117.226667 cu. ft<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 4 ,h = 7<br \/>\nv = 3.14 x 4 x 4 x (7\/3)<br \/>\nv = 3.14 x 16 x (7\/3)<br \/>\nv =3.14 x 16 x 2.3333<br \/>\nv= 3.14 x 37.33333<br \/>\nv = 117.226667 cu. ft<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30696\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-21.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 21\" width=\"117\" height=\"121\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone =65.416666 cu. in<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 2.5 ,h = 10<br \/>\nv = 3.14 x 2.5 x 2.5 x (10\/3)<br \/>\nv = 3.14 x 6.25 x (10\/3)<br \/>\nv =3.14 x 6.25 x 3.33<br \/>\nv= 3.14 x 20.8333<br \/>\nv = 65.416666 cu. in<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30697\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-22.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 22\" width=\"94\" height=\"131\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone =1.5 cu. cm<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 2 ,h = 8<br \/>\nv = 3.14 x 2 x 2x (8\/3)<br \/>\nv = 3.14 x 4 x (8\/3)<br \/>\nv =3.14 x 4 x 2.666<br \/>\nv= 3.14 x 10.6666<br \/>\nv = 1.5 cu. cm<\/p>\n<p><span style=\"font-size: 16px;\">Question 18.<\/span><\/p>\n<p><strong>STRUCTURE<\/strong><br \/>\nThe inside of each glass is shaped like a cone. Which glass can hold more liquid? How much more?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30698\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-23.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 23\" width=\"262\" height=\"145\" \/><\/p>\n<p>Answer:<br \/>\nGlass A can hold more liquid than glass B.<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 Glass A =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 4 ,h = 8<br \/>\nv = 3.14 x 4 x 4 x (8\/3)<br \/>\nv = 3.14 x 16 x (8\/3)<br \/>\nv =3.14 x 16 x 2.666<br \/>\nv= 3.14 x 42.656<br \/>\nv = 42.656 cu. cm<br \/>\nvolume of\u00a0 Glass A =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 3 ,h = 10<br \/>\nv = 3.14 x 3 x 3 x (10\/3)<br \/>\nv = 3.14 x 9 x (10\/3)<br \/>\nv =3.14 x 9 x 3.33<br \/>\nv= 3.14 x 30<br \/>\nv = 94.2 cu. cm<\/p>\n<p><strong>FINDING A MISSING DIMENSION OF A CONE<\/strong> Find the missing dimension of the cone. Round your answer to the nearest tenth.<br \/>\nQuestion 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30699\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-24.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 24\" width=\"139\" height=\"151\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cone = 9203 cubic cm<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that\u00a0 r=0.33 ,v = (1\/18) ,v = 0.055<br \/>\n0.055 = 3.14 x 0.33 x 0.33 x (h\/3)<br \/>\n0.055 = 3.14 x 0.1089h<br \/>\n0.055 =0.341946 h<br \/>\nh =(8788\/3) x 3.14<br \/>\nh = 2929.33 x 3.14<br \/>\nh = 9203 cubic cm<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30700\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-25.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 25\" width=\"139\" height=\"144\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cone = 0.1162963 cu. cm<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that\u00a0 r=5 ,v = 225<br \/>\n225 = 3.14 x 5 x 5 x (h\/3)<br \/>\n225 = 3.14 x 5 x 1.666 h<br \/>\n225 =8.3333 x 3.14 h<br \/>\n225 = 26.1666666 h<br \/>\nh = (26.1666666\/225)<br \/>\nh = 0.1162963 sq cm<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30701\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-26.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 26\" width=\"126\" height=\"143\" \/><\/p>\n<p>Answer:<br \/>\nradius of cone =\u00a0 3.15 cubic in<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that\u00a0 h= 4.2 ,v = 3.6<br \/>\n3.6 = 3.14 x r x r x (4.2\/3)<br \/>\n3.6 = 3.14 x r\u00b2 \u00a0 x 1.4<br \/>\n3.6\u00a0 =( 4.396 \/ r\u00b2 )<br \/>\nr\u00b2 \u00a0= 3\/4 x h<br \/>\nr = 0.75 x 4.12<br \/>\nr = 3.15\u00a0 cubic in<\/p>\n<p>Question 22.<br \/>\n<strong>FINDING A MISSING DIMENSION OF A CONE<\/strong><br \/>\nThe volume of a cone with a height of 10 meters is 20\u03c0 cubic meters. What is the diameter of the cone?<\/p>\n<p>Answer:<br \/>\ndiameter of cone = 0.333 meters<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that\u00a0 h= 10 ,v = 20<br \/>\n20 = 3.14 x r x r x (10\/3)<br \/>\n20 = 3.14 x r\u00b2 \u00a0 x3.33<br \/>\n20\u00a0 = 10.46666 r\u00b2<br \/>\nr\u00b2 \u00a0= 0.1665\u00a0 x 2<br \/>\nr = 0.333 meters.<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nWater leaks from a crack in a cone-shaped vase at a rate of 0.5 cubic inch per minute. The vase has a height of 10 inches and a diameter of 4.8 inches. How long does it take for 20% of the water to leak from the vase when it is full of water?<\/p>\n<p>Answer:<br \/>\n20% of water to leak from the vase when it is full of water = 1206.4<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 2.4 ,h = 10<br \/>\nv = 3.14 x 2.4 x 2.4 x (10\/3)<br \/>\nv = 3.14 x 5.76\u00a0 x (10\/3)<br \/>\nv =3.14 x 5.76 x 3.33<br \/>\nv= 3.14 x 384<br \/>\nv = 1206.4<br \/>\n20% of water to leak from the vase when it was full of water<br \/>\n1206.4<\/p>\n<p>Question 24.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou have 10 gallons of lemonade to sell. (1 gal \u2248 3785 cm<sup>3<\/sup>)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30702\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-27.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 27\" width=\"306\" height=\"150\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-27.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-27-300x147.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\na. Each customer uses 1 paper cup. The cups are sold in packages of 50. How many packages should you buy?<br \/>\nb. How many cups will be left over if you sell 80% of the lemonade?<\/p>\n<p>Answer:<br \/>\na. the no of packages should buy = 25<br \/>\nb. 20 cups will be left over if we sell 80% of lemonade.<\/p>\n<p>Explanation:<br \/>\na. the no of packages = 25<br \/>\nIn the question given that the cups are sold in the packages of 50<br \/>\nb. 80% of cups will be left in the lemonade = 20<br \/>\n100 &#8211; 80 =\u00a0 20<\/p>\n<p>Question 25.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nThe cylinder and the cone have the same volume. What is the height of the cone?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30703\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-28.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 28\" width=\"200\" height=\"134\" \/><\/p>\n<p>Answer:<br \/>\nThe height of the cone = 54 \u03c0<\/p>\n<p>Explanation:<br \/>\nGiven that the cone and the cylinder have the same volume.<br \/>\nThe height of the cone = 54 \u03c0<br \/>\n54 x 3.14<br \/>\n169.56<br \/>\n170 cubic cm<\/p>\n<p>Question 26.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIn Example 4, you use a different timer with the same dimensions. The sand in this timer has a height of 30 millimeters. How much time do you have to answer the question?<\/p>\n<p>Answer:<br \/>\n300 minutes will take to answer the question.<\/p>\n<p>Explanation:<br \/>\nThe sand in this timer has a height of 30 mm<br \/>\ntime to answer the question = 5 x 6<br \/>\n5 hrs<br \/>\n300 minutes will take to answer the question.<\/p>\n<p>Question 27.<br \/>\n<strong>REASONING<\/strong><br \/>\nA vapor cone is a cloud of condensed water that forms when an aircraft breaks the sound barrier. How does doubling both the diameter and the height affect the volume of the vapor cone?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30704\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-10.2-29.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids 10.2 29\" width=\"164\" height=\"129\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the vapor cone is changed.<\/p>\n<p>Explanation:<br \/>\nthe volume of the cone = 4\/3 \u03c0r\u00b3<br \/>\nv =4\/3 \u03c0r\u00b3<br \/>\nr = 3\u221a 435,750,000<br \/>\n3200 + 3\u221a 435,750,000<br \/>\n3958<\/p>\n<h3><a id=\"Lesson_10.3_Volumes_of_Spheres\"><\/a>Lesson 10.3 Volumes of Spheres<\/h3>\n<p>A sphere is the set of all points in space that are the same distance from a point called the center. The radius r is the distance from the center to any point on the sphere. A sphere is different from the other solids you have studied so far because it does not have a base.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30705\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 1\" width=\"208\" height=\"134\" \/><\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Finding a Formula Experimentally<br \/>\nWork with a partner. Use a plastic ball similar to the one shown. Draw a net for a cylinder with a diameter and a height equal to the diameter of the ball. Then cut out the net and use tape to form an open cylinder.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30706\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-2.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 2\" width=\"207\" height=\"421\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-2.png 207w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-2-148x300.png 148w\" sizes=\"(max-width: 207px) 100vw, 207px\" \/><br \/>\na. How is the height h of the cylinder related to the radius r of the ball?<br \/>\nb. Cover the ball with aluminum foil or tape. Leave one hole open. Fill the ball with rice. Then pour the rice into the cylinder. What fraction of the cylinder is filled with rice?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30707\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-3.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 3\" width=\"141\" height=\"159\" \/><br \/>\nc. Use your result in part(b) and the formula for the volume of a cylinder to write a formula for the volume of a sphere. Explain your reasoning.<\/p>\n<p>Answer:<br \/>\na. Height of the cylinder is proportional to the radius of the ball.<br \/>\nc. volume of cylinder = \u03c0r\u00b2h<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-30708\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-4.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 4\" width=\"192\" height=\"83\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the volume of the sphere. Round your answer to the nearest tenth.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30709\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-5.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 5\" width=\"122\" height=\"117\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere = 33.49333 cubic mm<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv = (4\/3) x 3.14 x 2 x 2 x2<br \/>\nwhere r = 2 given<br \/>\nv = 1.33 x 3.14 x 8<br \/>\nv= 4.18666 x 8<br \/>\nv = 33.49333 cubic mm<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30710\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-6.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 6\" width=\"136\" height=\"121\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere =2,138.2144 sq ft<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv = (4\/3) x 3.14 x 8 x 8 x8<br \/>\nwhere r = 8\u00a0 given<br \/>\nv = 1.33 x 3.14 x 512<br \/>\nv= 1.33 x 1,607.68<br \/>\nv = 2,138.2144 cu. ft<\/p>\n<p><strong>Find the radius of the sphere. Round your answer to the nearest tenth if necessary.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30711\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-7.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 7\" width=\"139\" height=\"143\" \/><\/p>\n<p>Answer:<br \/>\nradius of the sphere=0.333055310396 m<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\n36\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere v = 36<br \/>\n36 = 1.33r\u00b3<br \/>\nr\u00b3 = (1.33\/36)<br \/>\nr\u00b3 = 0.036944<br \/>\nr =0.333055310396 m<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30713\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-8.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 8\" width=\"124\" height=\"148\" \/><\/p>\n<p>Answer:<br \/>\nradius of the sphere= 0.6681660696 in<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\n14\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere v = 14<br \/>\n14 = 1.33 x 3.14 r\u00b3<br \/>\n14 = 4.1762 r\u00b3<br \/>\nr\u00b3 = (4.1762\/14)<br \/>\nr\u00b3 = 0.2983 cubic in<br \/>\nr = 0.6681660696 in<\/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>FINDING THE VOLUME OF A SPHERE<\/strong><br \/>\nFind the volume of the sphere. Round your answer to the nearest tenth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30714\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-9.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 9\" width=\"131\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere =17,105.7552 cu. cm<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv = (4\/3) x 3.14 x 16 x 16 x 16<br \/>\nwhere r = 16\u00a0 given<br \/>\nv = 1.33 x 3.14 x 4,096<br \/>\nv= 1.33 x 12,861.44<br \/>\nv = 17,105.7552 cu. cm<\/p>\n<p>Question 6.<br \/>\n<strong>FINDING THE RADIUS OF A SPHERE<\/strong><br \/>\nFind the radius of a sphere with a volume of 4500\u03c0 cubic yards.<\/p>\n<p>Answer:<br \/>\nradius of the sphere= 0.00029556 sq yds<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\n4500\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere v = 4500<br \/>\n4500 = 1.33 x 3.14 r\u00b3<br \/>\n4500 = 1.33 r\u00b3<br \/>\nr\u00b3 = (1.33\/4500)<br \/>\nr\u00b3 = 0.00029556<\/p>\n<p>Question 7.<br \/>\n<strong>WHICH ONE DOESN&#8217;T BELONG?<\/strong><br \/>\nWhich figure does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30715\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-10.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 10\" width=\"456\" height=\"96\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-10.png 456w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-10-300x63.png 300w\" sizes=\"(max-width: 456px) 100vw, 456px\" \/><\/p>\n<p>Answer:<br \/>\nsphere does not belong with the other three.<\/p>\n<p>Explanation:<br \/>\npyramid, prism, cylinder have bases.<br \/>\nsphere does not have a base.<\/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 8.<br \/>\nIn sphering, a person is secured inside a small, hollow sphere that is surrounded by a larger sphere. The space between the spheres is inflated with air. What is the volume of the inflated space? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30716\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-11.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 11\" width=\"174\" height=\"115\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the inflated surface = 79.54649 cu. m<\/p>\n<p>Explanation:<br \/>\nThe volume of larger sphere = (4\/3) \u03c0r\u00b3<br \/>\nv = (4\/3) x 3.14 x 3\u00b3<br \/>\nv = 1.333 x 3.14 x 27<br \/>\nv = 4.18666 x 27<br \/>\nv = 113.03982 cu. m<br \/>\nThe volume of hollow sphere = (4\/3) \u03c0r\u00b3<br \/>\nv = (4\/3) x 3.14 x 2\u00b3<br \/>\nv = 1.333 x 3.14 x 8<br \/>\nv = 4.18666 x 8<br \/>\nv = 33.49333 cu. m<br \/>\ninflated space = larger sphere &#8211; hollow sphere<br \/>\ninflated space = 79.54649<\/p>\n<p>Question 9.<\/p>\n<p><strong>DIG DEEPER!<\/strong><br \/>\nA vendor sells cones filled with frozen yogurt, as shown. The vendor has 4 cylindrical containers of frozen yogurt, each with a diameter of 18 centimeters and a height of 15 centimeters. About how much money will the vendor make when all of the frozen yogurt is sold? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30717\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-12.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 12\" width=\"130\" height=\"193\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone= 113.04 cu. cm<\/p>\n<p>Explanation:<br \/>\nthe volume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 3 ,h = 12<br \/>\nv = 3.14 x 3 x 3 x (12\/3)<br \/>\nv = 3.14 x 9\u00a0 x (12\/3)<br \/>\nv =3.14 x 9 x 4<br \/>\nv= 3.14 x 36<br \/>\nv = 113.04 cu. cm<\/p>\n<h3><a id=\"Volumes_of_Spheres_Homework_&amp;_Practice_10.3\"><\/a>Volumes of Spheres Homework &amp; Practice 10.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the volume of the cone. Round your answer to the nearest tenth.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30718\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-13.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 13\" width=\"110\" height=\"129\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone= 25.12 cu. ft<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 2 ,h = 6<br \/>\nv = 3.14 x 2 x 2 x (6\/3)<br \/>\nv = 3.14 x 4\u00a0 x (6\/3)<br \/>\nv =3.14 x 4 x 2<br \/>\nv= 3.14 x 8<br \/>\nv = 25.12 cu. ft<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30719\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-14.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 14\" width=\"126\" height=\"114\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone= 47.1 cu. cm<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 3 ,h = 5<br \/>\nv = 3.14 x 3 x 3 x (5\/3)<br \/>\nv = 3.14 x 9\u00a0 x (5\/3)<br \/>\nv =3.14 x 9 x 1.666<br \/>\nv= 3.14 x 15<br \/>\nv = 47.1 cu. cm<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30720\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-15.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 15\" width=\"150\" height=\"98\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone=84.78 cu. m<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 4.5 ,h = 4<br \/>\nv = 3.14 x 4.5 x 4.5 x (4\/3)<br \/>\nv = 3.14 x 20.25 x (4\/3)<br \/>\nv =3.14 x 20.25 x 1.333<br \/>\nv= 3.14 x 27<br \/>\nv = 84.78 cu. m<\/p>\n<p><strong>Evaluate the expression. Write your answer in scientific notation.<\/strong><br \/>\nQuestion 4.<br \/>\n(4.6 \u00d7 10<sup>9<\/sup>) + (3.9 \u00d7 10<sup>9<\/sup>)<\/p>\n<p>Answer:<br \/>\n85,00,00,00000<\/p>\n<p>Explanation:<br \/>\n(4.6 \u00d7 10<sup>9<\/sup>) + (3.9 \u00d7 10<sup>9<\/sup>)<br \/>\n4.6 x 1000000000 + 3.9 x 1000000000<br \/>\n85,00,00,00000<\/p>\n<p>Question 5.<br \/>\n(1.4 \u00d7 10<sup>-4<\/sup>) \u00f7 (2.8 \u00d7 10<sup>6<\/sup>)<\/p>\n<p>Answer:<br \/>\n5e &#8211; 12<\/p>\n<p>Explanation:<br \/>\n0.00014 \/ 28000000<br \/>\n5e &#8211; 12<\/p>\n<p>Question 6.<br \/>\nA person who is 5 feet tall casts a 6-foot-long shadow. A nearby flag pole casts a 30-foot-long shadow. What is the height of the flagpole?<br \/>\nA. 25 ft<br \/>\nB. 29 ft<br \/>\nC. 36 ft<br \/>\nD. 40 ft<br \/>\nAnswer:<br \/>\nOption B is correct.<\/p>\n<p>Explanation:<br \/>\nGiven that person who is 5 feet tall casts a 6-foot-long shadow.<br \/>\nA nearby flag pole casts a 30-foot-long shadow.<br \/>\nthe height of the flagpole is 29 ft<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>FINDING VOLUME<\/strong> The radius of a sphere is given. Find the volume of the sphere. Write your answer in terms of \u03c0. (See Exploration 1, p. 439.)<br \/>\nQuestion 7.<br \/>\nr = 6 units<\/p>\n<p>Answer:<br \/>\nvolume of the sphere= 902.0592 units<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =6<br \/>\nv = 1.33 x 3.14\u00a0 x 6 x 6 x 6<br \/>\nv = 1.33 x 3.14 x 216<br \/>\nv = 1.33 x 678.24<br \/>\nv = 902.0592 units<\/p>\n<p>Question 8.<br \/>\nr = 12 units<\/p>\n<p>Answer:<br \/>\nvolume of the sphere= 7,216.4736 units<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =12<br \/>\nv = 1.33 x 3.14\u00a0 x 12 x 12 x 12<br \/>\nv = 1.33 x 3.14 x 1,728<br \/>\nv = 1.33 x 5,425.92<br \/>\nv = 7,216.4736 units<\/p>\n<p>Question 9.<br \/>\nr = 10 units<\/p>\n<p>Answer:<br \/>\nvolume of the sphere=4,176.2 units<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =10<br \/>\nv = 1.33 x 3.14\u00a0 x 10 x 10 x 10<br \/>\nv = 1.33 x 3.14 x 1000<br \/>\nv = 1.33 x 3140<br \/>\nv = 4,176.2 units<\/p>\n<p><strong>FINDING THE VOLUME OF A SPHERE<\/strong> Find the volume of the sphere. Round your answer to the nearest tenth.<br \/>\nQuestion 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30721\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-16.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 16\" width=\"126\" height=\"114\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere= 522.025 cu. units<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =5<br \/>\nv = 1.33 x 3.14\u00a0 x 5 x 5 x 5<br \/>\nv = 1.33 x 3.14 x 125<br \/>\nv = 1.33 x 3.92.5<br \/>\nv = 522.025 cu. units<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30722\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-17.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 17\" width=\"115\" height=\"113\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere=1,432.4366 cu. units<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =7<br \/>\nv = 1.33 x 3.14\u00a0 x 7 x 7 x 7<br \/>\nv = 1.33 x 3.14 x 343<br \/>\nv = 1.33 x 1,077.02<br \/>\nv = 1,432.4366 cu. units<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30724\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-18.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 18\" width=\"122\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere= 3,044.4498 units<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =9<br \/>\nv = 1.33 x 3.14\u00a0 x 9 x 9 x 9<br \/>\nv = 1.33 x 3.14 x 729<br \/>\nv = 1.33 x 2,289.06<br \/>\nv = 3,044.4498 cu. units<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30725\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-19.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 19\" width=\"118\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere= 300.6864 cu. units<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =6<br \/>\nv = 1.33 x 3.14\u00a0 x 6 x 6 x 6<br \/>\nv = 1.33 x 3.14 x 72<br \/>\nv = 1.33 x 226.08<br \/>\nv = 300.6864 cu. units<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30726\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-20.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 20\" width=\"111\" height=\"116\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere= 112.7574 cu. units<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =3<br \/>\nv = 1.33 x 3.14\u00a0 x 3 x 3 x 3<br \/>\nv = 1.33 x 3.14 x 27<br \/>\nv = 1.33 x 84.78<br \/>\nv = 112.7574 cu. units<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30727\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-21.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 21\" width=\"133\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere=11,459.4928 cu. units<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =14<br \/>\nv = 1.33 x 3.14\u00a0 x 14 x 14 x 14<br \/>\nv = 1.33 x 3.14 x 2744<br \/>\nv = 1.33 x 8,616.16<br \/>\nv = 11,459.4928 cu. units<\/p>\n<p><strong>FINDING THE RADIUS OF A SPHERE<\/strong> Find the radius of a sphere with the given volume. Round your answer to the nearest tenth if necessary.<br \/>\nQuestion 16.<br \/>\nVolume = 972\u03c0 mm<sup>3<\/sup><\/p>\n<p>Answer:<br \/>\nradius of the sphere= 0.0004561\u00a0cubic mm<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\n972\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere v = 972<br \/>\n972 = 1.33 x 3.14 r\u00b3<br \/>\n972 = 1.33 r\u00b3<br \/>\nr\u00b3 = (1.33\/972)<br \/>\nr\u00b3 = 0.00136831 cubic mm<br \/>\nr = 0.0004561<\/p>\n<p>Question 17.<br \/>\nVolume = 4.5\u03c0 cm<sup>3<\/sup><\/p>\n<p>Answer:<br \/>\nradius of the sphere= 0.09851852 cubic cm<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\n4.5\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere v = 4.5<br \/>\n4.5 = 1.33 x 3.14 r\u00b3<br \/>\n4.5 = 1.33 r\u00b3<br \/>\nr\u00b3 = (1.33\/4.5)<br \/>\nr\u00b3 = 0.29555555 cubic mm<br \/>\nr = 0.09851852 cubic cm<\/p>\n<p>Question 18.<br \/>\nVolume = 180 ft<sup>3<\/sup><\/p>\n<p>Answer:<br \/>\nradius of the sphere=0.0077337 cubic ft<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\n180 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere v = 180<br \/>\n180 = 1.33 x 3.14 r\u00b3<br \/>\n180 = 1.33\u00a0 x 3.14r\u00b3<br \/>\n180 = 4.1762 r\u00b3<br \/>\nr\u00b3 = (4.1762\/180)<br \/>\nr\u00b3 = 0.02320111 cubic ft<br \/>\nr = 0.0077337 cubic ft<\/p>\n<p>Question 19.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe globe of the moon has a radius of 13 centimeters. Find the volume of the globe. Round your answer to the nearest whole number.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30728\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-22.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 22\" width=\"159\" height=\"230\" \/><\/p>\n<p>Answer:<br \/>\nVolume of the globe =9,175.1114 cu. cm<\/p>\n<p>Explanation:<br \/>\nvolume of the globe=11,459.4928 units<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =13<br \/>\nv = 1.33 x 3.14\u00a0 x 13 x 13 x 13<br \/>\nv = 1.33 x 3.14 x 2,197<br \/>\nv = 1.33 x 6,898.58<br \/>\nv = 9,175.1114 cu. cm<\/p>\n<p>Question 20.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA softball has a volume of about 29 cubic inches. Find the radius of the softball. Round your answer to the nearest tenth.<\/p>\n<p>Answer:<br \/>\nradius of the softball= 0.0480023 ft<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\n29= (4\/3) x 3.14 x r\u00b3<br \/>\nwhere v = 29<br \/>\n29 = 1.33 x 3.14 r\u00b3<br \/>\n29 = 1.33\u00a0 x 3.14r\u00b3<br \/>\n29 = 4.1762 r\u00b3<br \/>\nr\u00b3 = (4.1762\/29)<br \/>\nr\u00b3 = 0.1440069 cubic ft<br \/>\nr = 0.0480023 ft<\/p>\n<p>Question 21.<br \/>\n<strong>REASONING<\/strong><br \/>\nA sphere and a right cylinder have the same radius and volume. Find the radius r in terms of the height h of the cylinder.<\/p>\n<p>Answer:<br \/>\nThe volume of sphere = (4\/3) \u03c0 h\u00b3<br \/>\nthe volume of cylinder = \u03c0r\u00b2 \u00a0r<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0 r\u00b3<br \/>\nThey said to find the radius r in terms of height h.<br \/>\nthe volume of sphere = (4\/3) \u03c0 h\u00b3<br \/>\nthe volume of cylinder = \u03c0r\u00b2 r<\/p>\n<p><strong>FINDING VOLUME<\/strong> Find the volume of the composite solid. Round your answer to the nearest tenth.<br \/>\nQuestion 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30729\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-23.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 23\" width=\"157\" height=\"144\" \/><\/p>\n<p>Answer:<br \/>\nvolume = 256 cubic cm<\/p>\n<p>Explanation:<br \/>\nvolume of rectangular prism = lwh<br \/>\nwhere l= length, w = weight, h= height<br \/>\nl = 8 ,w = 8 , h = 8 given<br \/>\nv= 8 x 8 x 8<br \/>\nv = 64 x 4<br \/>\nv =\u00a0 256 cubic cm<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30730\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-24.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 24\" width=\"163\" height=\"131\" \/><\/p>\n<p>Answer:<br \/>\nvolume = 192 cubic feet<\/p>\n<p>Explanation:<br \/>\nvolume of triangular prism = (bhl\/2)<br \/>\nb = 16 , h = 6 , l = 4 given<br \/>\nv = (16 x 6 x 4\/2)<br \/>\nv = (16 x 24\/2)<br \/>\nv = 16 x 12<br \/>\nv = 192 cubic feet<\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30731\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-25.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 25\" width=\"129\" height=\"150\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cylinder = 310.86 cu. in<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nv = 3.14 x 3 x 3 x 11<br \/>\nv = 3.14 x 9 x 11<br \/>\nv = 3.14 x 99<br \/>\nv = 310.86 cu. in<\/p>\n<p>Question 25.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA cylindrical container of three rubber balls has a height of 18 centimeters and a diameter of 6 centimeters. Each ball in the container has a radius of 3 centimeters. Find the amount of space in the container that is not occupied by rubber balls. Round your answer to the nearest whole number.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30732\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-26.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 26\" width=\"110\" height=\"188\" \/><br \/>\nAnswer:<br \/>\nThe amount of space in the container that is not occupied by the rubber balls = 2,034.72 cu. cm<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nv = 3.14 x 6 x 6 x 18<br \/>\nv = 3.14 x 36 x 18<br \/>\nv = 3.14 x 648<br \/>\nv =2,034.72 cu. cm<\/p>\n<p>Question 26.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe basketball shown is packaged in a box that is in the shape of a cube. The edge length of the box is equal to the diameter of the basketball. What are the surface area and the volume of the box?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30733\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-27.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 27\" width=\"157\" height=\"138\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of sph0.01646091 cubic in<\/p>\n<p>Explanation:<br \/>\nthe volume of sphere = 4 \u03c0r\u00b2<br \/>\n121.5 \u03c0 = 4 \u03c0 r\u00b2<br \/>\n121.5 = 4 r\u00b2<br \/>\nr\u00b2 = (4\/121.5)<br \/>\nr\u00b2 = 0.03292181<br \/>\nr = 0.01646091 cubic in<\/p>\n<p>Question 27.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe inner core of Earth begins about 3200 miles below the surface of Earth and has a volume of about 581,000,000\u03c0 cubic miles. Approximate the radius of Earth. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30734\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.3-28.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids 10.3 28\" width=\"257\" height=\"206\" \/><\/p>\n<p>Answer:<br \/>\nradius\u00a0 of earth = 0.00240199 miles.<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0 r\u00b3<br \/>\n581,000,000 \u03c0\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\n581,000,000= 1.3333 x 3.14 x r\u00b3<br \/>\n581,000,000= 4.18666667 \u00a0r\u00b3<br \/>\nr\u00b3 = (4.18666667\/581.000,000)<br \/>\nr\u00b3 = 0.00720597<br \/>\nr = 0.00240199 miles,<\/p>\n<p>Question 28.<br \/>\n<strong>LOGIC<\/strong><br \/>\nYour friend says that the volume of a sphere with radius r is four times the volume of a cone with radius r. When is this true? Justify your answer.<br \/>\nAnswer:<br \/>\nNo my friend is wrong.<\/p>\n<p>Explanation:<br \/>\nvolume of cone = \u03c0r\u00b2 (h\/3)<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nwhen the radius is equal to the height h<br \/>\nthen the volume of a sphere with radius r is four times the volume of a cone with a radius r.<\/p>\n<h3><a id=\"Lesson_10.4_Surface_Areas_and_Volumes_of_Similar_Solids\"><\/a>Lesson 10.4 Surface Areas and Volumes of Similar Solids<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Comparing Similar Solids<br \/>\nWork with a partner.<br \/>\na.You multiply the dimensions of the smallest cylinder by different factors to create the other four cylinders. Complete the table. Compare the surface area and volume of each cylinder with the surface area and volume of the smallest cylinder.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30735\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-1.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 1\" width=\"489\" height=\"259\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-1.png 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-1-300x159.png 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\nb. Repeat part(a) using the square pyramids and table below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30736\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-2.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 2\" width=\"658\" height=\"278\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-2.png 658w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-2-300x127.png 300w\" sizes=\"(max-width: 658px) 100vw, 658px\" \/><\/p>\n<p>Answer:<br \/>\na.\u00a0 surface area of cylinder\u00a0 1 = 12.56<br \/>\nb. surface area of cylinder\u00a0 2 = 50.24<br \/>\nc. surface area of cylinder\u00a0 3 = 113.04<br \/>\nd. surface area of cylinder\u00a0 4 = 200.96<br \/>\ne.. surface area of cylinder\u00a0 5 = 314<\/p>\n<p>Explanation:<br \/>\na. surface area of cylinder\u00a0 1 = 2 \u03c0r\u00b2 + 2 \u03c0rh<br \/>\nA = 2 x 3.14 x 1 + 2 x 3.14 x 1 x 1<br \/>\nA = 6.28 + 6.28<br \/>\nA = 12.56<br \/>\nvolume of cylinder = \u03c0r\u00b2h<br \/>\nv = 3.14 x 1 x 1<br \/>\nv = 3.14<br \/>\nb. surface area of cylinder\u00a0 2 = 2 \u03c0r\u00b2 + 2 \u03c0rh<br \/>\nA = 2 x 3.14 x 2 x 2 + 2 x 3.14 x 2 x 2<br \/>\nA = 6.28 x 4 + 6.28 x 4<br \/>\nA = 25.12 + 25.12<br \/>\nA = 50.24<br \/>\nvolume of cylinder = \u03c0r\u00b2h<br \/>\nv = 3.14 x 2 x 2<br \/>\nv = 3.14 x 4<br \/>\nv = 12.56<br \/>\nc. surface area of cylinder\u00a0 1 = 2 \u03c0r\u00b2 + 2 \u03c0rh<br \/>\nA = 2 x 3.14 x 3 x 3 + 2 x 3.14 x 3 x 3<br \/>\nA = 6.28 x 9 + 6.28 x 9<br \/>\nA = 56.52 +56.52<br \/>\nA = 113.04<br \/>\nvolume of cylinder = \u03c0r\u00b2h<br \/>\nv = 3.14 x 3 x 3<br \/>\nv = 3.14 x 9<br \/>\nv = 28.26<br \/>\nd. surface area of cylinder\u00a0 1 = 2 \u03c0r\u00b2 + 2 \u03c0rh<br \/>\nA = 2 x 3.14 x 4 x 4 + 2 x 3.14 x 4 x 4<br \/>\nA = 6.28 x 16 + 6.28 x 16<br \/>\nA = 100.48 + 100.48<br \/>\nA = 200.96<br \/>\nvolume of cylinder = \u03c0r\u00b2h<br \/>\nv = 3.14 x 4 x 4<br \/>\nv = 3.14 x 16<br \/>\nv = 50.24<br \/>\ne. surface area of cylinder\u00a0 1 = 2 \u03c0r\u00b2 + 2 \u03c0rh<br \/>\nA = 2 x 3.14 x 5 x 5 + 2 x 3.14 x 5 x 5<br \/>\nA = 6.28 x 25 + 6.28 x 25<br \/>\nA = 157 + 157<br \/>\nA = 314<br \/>\nvolume of cylinder = \u03c0r\u00b2h<br \/>\nv = 3.14 x 5 x 5<br \/>\nv = 3.14 x 25<br \/>\nv = 78.5<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-30737\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-3.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 3\" width=\"190\" height=\"68\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nCylinder D has a radius of 7.5 meters and a height of 4.5 meters. Which cylinder in Example 1 is similar to Cylinder D?<\/p>\n<p>Answer:<br \/>\nvolume of cylinder = 794.8125 cu. meters.<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2h<br \/>\nv = 3.14 x 7.5 x 7.5 x 4.5<br \/>\nv = 3.14 x 56.25 x 4.5<br \/>\nv = 3.14 x 253.125<br \/>\nv = 794.8125 cu. meters.<\/p>\n<p>Question 2.<br \/>\nThe prisms at the right are similar. Find the missing width and length.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30738\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-4.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 4\" width=\"201\" height=\"121\" \/><\/p>\n<p>Answer:<br \/>\nvolume = 1760 cubic in<\/p>\n<p>Explanation:<br \/>\nthe volume of rectangular prism = lwh<br \/>\nwhere l= length, w = weight, h= height<br \/>\nl = 11,w = 8 , h = 20 given<br \/>\nv= 11 x 8 x 20<br \/>\nv = 88 x 20<br \/>\nv =\u00a0 1760 cubic in<\/p>\n<p><strong>The solids are similar. Find the surface area of the red solid. Round your answer to the nearest tenth.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30739\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-5.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 5\" width=\"203\" height=\"144\" \/><\/p>\n<p>Answer:<br \/>\nvolume = 440 cubic m<\/p>\n<p>Explanation:<br \/>\nvolume of rectangular prism = lwh<br \/>\nwhere l= length, w = weight, h= height<br \/>\nl\u00a0 = 11,w = 8 , h = 5 given<br \/>\nv= 11 x 8x 5<br \/>\nv = 11 x 40<br \/>\nv =\u00a0 440 cubic m<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30740\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-6.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 6\" width=\"204\" height=\"154\" \/><\/p>\n<p>Answer:<br \/>\nVolume of cylinder= 0.17840909 cu. cm<\/p>\n<p>Explanation:<br \/>\nVolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14<br \/>\nr = 2.5<br \/>\n110 = 3.14 x 2.5 x 2.5 x h<br \/>\n110 = 3.14 x 6.25 h<br \/>\n110= 19.625 h<br \/>\nh = (19.625\/110)<br \/>\nh = 0.17840909 sq cm<\/p>\n<p>Question 5.<br \/>\nThe pyramids at the left are similar. Find the volume of the red pyramid. Round your answer to the nearest tenth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30741\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-7.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 7\" width=\"219\" height=\"107\" \/><\/p>\n<p>Answer:<br \/>\nvolume of red pyramid = 0.444 cubic in<\/p>\n<p>Explanation:<br \/>\nthe volume of the pyramid =( l x w x h\/3)<br \/>\nv = 9 given, width = 4 h = 3<br \/>\n9=( 4 x 3h \/3)<br \/>\n9 = 4h<br \/>\nh = (4\/9)<br \/>\nh = 0.444 cubic in<\/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 6.<br \/>\n<strong>IDENTIFYING SIMILAR SOLIDS<\/strong><br \/>\nCone A and Cone B are right cones. Cone B has a radius of 1.25 feet and a height of 3 feet. Are the cones similar?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30742\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-8.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 8\" width=\"169\" height=\"75\" \/><\/p>\n<p>Answer:<br \/>\nNo the cones are not similar.<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 A =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 5 ,h = 12<br \/>\nv = 3.14 x 5 x 5 x (12\/3)<br \/>\nv = 3.14 x 25 x (12\/3)<br \/>\nv =3.14 x 25 x 4<br \/>\nv= 3.14 x100<br \/>\nv = 314\u00a0 cu. ft<br \/>\nvolume of\u00a0 cone\u00a0 B =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 1.25 ,h = 3<br \/>\nv = 3.14 x 1.25 x 1.25 x (3\/3)<br \/>\nv = 3.14 x 1.5625 x (3\/3)<br \/>\nv =3.14 x 1.5625 x 1<br \/>\nv= 3.14 x1.5625<br \/>\nv = 4.90625 cu. ft<\/p>\n<p>Question 7.<br \/>\n<strong>FINDING A MISSING MEASURE<\/strong><br \/>\nA cylinder with a radius of 4 inches r and a height of 6 inches is similar to a cylinder with a radius of r inches and a height of 9 inches. What is the value of r?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30743\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-9.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 9\" width=\"176\" height=\"148\" \/><\/p>\n<p>Answer:<br \/>\nThe value of r = 3 yds<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cylinder\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 4 ,h = 6<br \/>\nv = 3.14 x 4 x 4 x (6\/3)<br \/>\nv = 3.14 x 16 x (6\/3)<br \/>\nv =3.14 x 16 x 2<br \/>\nv= 3.14 x 32<br \/>\nv = 100.48<\/p>\n<p>Question 8.<br \/>\n<strong>FINDING SURFACE AREA AND VOLUME<\/strong><br \/>\nThe rectangular prisms shown are similar. Find the surface area and volume of the red rectangular prism .<\/p>\n<p>Answer:<br \/>\nThe surface area of rectangular prism =2(lw +lh +wh)<br \/>\nthe volume of rectangular prism = lwh<\/p>\n<p>Explanation:<br \/>\nThe surface area of rectangular prism =2(lw +lh +wh)<br \/>\nwhere h = height, w = width, l = length<br \/>\nthe volume of rectangular prism = lwh<\/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 \/>\nTwo snails have shells that are similar in shape. The younger snail has a shell with a height of 3.9 centimeters and a volume of 3 cubic centimeters. The older snail has a shell with a volume of 10 cubic centimeters. Estimate the height of the older snail\u2019s shell.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30744\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-10.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 10\" width=\"172\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\nThe height of the older snails shell = 0.942 cm<\/p>\n<p>Explanation:<br \/>\nthe volume of\u00a0 cylinder\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 3 ,v = 10<br \/>\n10 = 3.14 x 3 x 3 x (h\/3)<br \/>\n10 = 3.14 x 3 x h<br \/>\n10 =3.14 x 3h<br \/>\n10= 9.42 h<br \/>\nh = (9.42\/10)<br \/>\nh = 0.942 cm<\/p>\n<p>Question 10.<br \/>\nTwo barrels filled with sand are similar in shape. The smaller barrel has a height of 4 feet and a volume of 4.5 cubic feet. The larger barrel has a height of 6 feet. What is the weight of the sand in the larger barrel? Round your answer to the nearest tenth.(One cubic foot of sand weighs about 110 pounds.)<\/p>\n<p>Answer:<br \/>\nThe weight of the sand in the larger barrel\u00a0 = 18 cubic feet<\/p>\n<p>Explanation:<br \/>\nGiven that the smaller barrel h = 4 ft and v = 4.5 cubic ft<br \/>\nweight = 4 x 4.5<br \/>\nweight = 18 cubic feet<br \/>\nlarger barrel h =\u00a0 6feet, v= 3 cubic feet,<br \/>\nweight = 3 x 6<br \/>\nweight = 18 cubic feet<br \/>\n1 cubic ft = 110 pounds<\/p>\n<p>Question 11.<br \/>\nTwo trunks are similar in shape. The larger trunk has a length of 6 feet and a surface area of 164.25 square feet. The smaller trunk has a length of 4 feet. The materials needed to manufacture each trunk cost $0.60 per square foot. What is the total cost of the materials needed to manufacture the smaller trunk?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Surface_Areas_and_Volumes_of_Similar_Solids_Homework_&amp;_Practice_10.4\"><\/a>Surface Areas and Volumes of Similar Solids Homework &amp; Practice 10.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the volume of the sphere. Round your answer to the nearest tenth.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30745\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-11.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 11\" width=\"131\" height=\"116\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere= 5,558.52222 cubic cm<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =11<br \/>\nv = 1.33 x 3.14\u00a0 x 11 x 11 x 11<br \/>\nv = 1.33 x 3.14 x 1,331<br \/>\nv = 1.33 x 4,179.34<br \/>\nv = 5,558.52222 cubic cm<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30746\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-12.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 12\" width=\"126\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere= 380.556225 cubic ft<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =4.5<br \/>\nv = 1.33 x 3.14\u00a0 x 4.5 x 4.5 x 4.5<br \/>\nv = 1.33 x 3.14 x 91.125<br \/>\nv = 1.33 x 286.1325<br \/>\nv = 380.556225 cubic ft<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30747\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-13.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 13\" width=\"122\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere=902.0592 cubic mm<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =6<br \/>\nv = 1.33 x 3.14\u00a0 x 6 x 6 x 6<br \/>\nv = 1.33 x 3.14 x 216<br \/>\nv = 1.33 x 678.24<br \/>\nv = 902.0592 cubic mm<\/p>\n<p>Question 4.<br \/>\nWhich system of linear equations has no solution?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30748\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-14.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 14\" width=\"540\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-14.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-14-300x35.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><br \/>\nAnswer:<br \/>\nOption c has no solution.<\/p>\n<p>Explanation:<br \/>\nif we take x = 2<br \/>\nA. y = 4x + 1 = 4(2) + 1= 9 , y = &#8211; 4x + 1 = -8 + 1= -7<br \/>\nb. Y = 2x &#8211; 7 = 4 &#8211; 7 = -3 , y = 2x + 7 = 4 + 7 = 11<br \/>\nc. 3x + y = 1 , y = 1 &#8211; 6 y = -5 , 6x + 2y = 2 = 12 + 2y = 2,2y =- 10\u00a0 y = -5<br \/>\n<strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>COMPARING SIMILAR SOLIDS<\/strong> All of the dimensions of the solid are multiplied by a factor of k. How many times greater is the surface area of the new solid? How many times greater is the volume of the new solid? (See Exploration 1, p. 445.)<br \/>\nQuestion 5.<br \/>\nk = 5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30749\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-15.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 15\" width=\"174\" height=\"122\" \/><\/p>\n<p>Answer:<br \/>\n25 times greater.<br \/>\nvolume of new solid = 125 cubic ft<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 prism = lwh<br \/>\nwhere l= length, w = weight, h= height<br \/>\nl = 5 ,w = 5 , h = 5 given<br \/>\nv= 5 x 5 x 5<br \/>\nv = 5 x 25<br \/>\nv =\u00a0 125\u00a0 cubic ft<\/p>\n<p>Question 6.<br \/>\nk = 10<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30750\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-16.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 16\" width=\"169\" height=\"107\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 new cone= 1,046.666 cubic cm<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 10 ,h = 10<br \/>\nv = 3.14 x 10 x 10 x (10\/3)<br \/>\nv = 3.14 x 100 x (10\/3)<br \/>\nv =3.14 x 100 x 3.33<br \/>\nv= 3.14 x 333.33<br \/>\nv = 1,046.666 cubic cm<\/p>\n<p><strong>IDENTIFYING SIMILAR SOLIDS<\/strong> Determine whether the solids are similar.<br \/>\nQuestion 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30751\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-17.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 17\" width=\"208\" height=\"151\" \/><\/p>\n<p>Answer:<br \/>\nThe solida are\u00a0 similar<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 small prism = lwh<br \/>\nwhere l= length, w = weight, h= height<br \/>\nl = 2 ,w = 1 , h = 3 given<br \/>\nv= 2 x 1 x 3<br \/>\nv = 2 x 3<br \/>\nv =\u00a0 6\u00a0 cubic in<br \/>\nvolume of\u00a0 large prism = lwh<br \/>\nwhere l= length, w = weight, h= height<br \/>\nl = 6 ,w = 3 , h = 9 given<br \/>\nv= 6 x 3 x 9<br \/>\nv = 2 x 27<br \/>\nv =\u00a0 54 cubic in<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30752\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-18.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 18\" width=\"240\" height=\"111\" \/><\/p>\n<p>Answer:<br \/>\nThe solida are not similar<\/p>\n<p>Explanation:<br \/>\nsurface area\u00a0 of\u00a0 large prism =2 (lw + wh +1h)<br \/>\nwhere l= length, w = weight, h= height<br \/>\nl = 4 ,w = 2 , h = 4 given<br \/>\nv=2( 4 x 2 + 2 x 4 + 4 x 4)<br \/>\nv = 2 (8 + 8+ 16)<br \/>\nv =\u00a0 2( 32)<br \/>\nv = 64 cubic in<br \/>\nsurface area\u00a0 of small prism =2 (lw + wh +1h)<br \/>\nwhere l= length, w = weight, h= height<br \/>\nl = 2 ,w = 1 , h = 4 given<br \/>\nv=2( 2 x 1 + 1 x 4 + 2 x 4)<br \/>\nv = 2 (2 + 4+ 8)<br \/>\nv =\u00a0 2( 16)<br \/>\nv = 32 cubic in<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30753\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-19.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 19\" width=\"233\" height=\"143\" \/><\/p>\n<p>Answer:<br \/>\nThe pyramids are\u00a0 similar.<\/p>\n<p>Explanation:<br \/>\nsurface area of triangular pyramid 1 = area of faces + base<br \/>\narea of face 1 = 5<br \/>\narea of face 2 = 5<br \/>\narea of face 3 = 6.5<br \/>\narea of face 4 = 6<br \/>\narea of base = 5<br \/>\nA= 5 + 5 + 6.5 + 6 + 5<br \/>\nA = 10 + 6.5 + 11<br \/>\nA = 21 + 6.5<br \/>\nA = 27.5<br \/>\nsurface area of triangular pyramid 2 = area of faces + base<br \/>\narea of face 1 = 10<br \/>\narea of face 2 = 10<br \/>\narea of face 3 = 13<br \/>\narea of face 4 = 12<br \/>\narea of base = 10<br \/>\nA= 10 + 10 + 13 + 12 + 10<br \/>\nA = 20 + 13 + 22<br \/>\nA = 42 + 13<br \/>\nA = 55<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30754\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-20.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 20\" width=\"255\" height=\"142\" \/><\/p>\n<p>Answer:<br \/>\nTwo solids are not similar.<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone 1 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that\u00a0 r=9 ,h = 12<br \/>\nv = 3.14 x 9 x 9 x (12\/3)<br \/>\nv = 3.14 x 9 x9 x 4<br \/>\nv =3.14 x 81 x 4<br \/>\nv = 3.14 x 324<br \/>\nh = 1,017.36sq m<br \/>\nvolume of\u00a0 cone 2 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that\u00a0 r=20 ,h = 21<br \/>\nv = 3.14 x 20 x 20 x (21\/3)<br \/>\nv = 3.14 x20 x 20 x 7<br \/>\nv =3.14 x 400 x 7<br \/>\nv = 3.14 x 2800<br \/>\nh =\u00a0 8,792 sq m<\/p>\n<p><strong>FINDING MISSING MEASURES IN SIMILAR SOLIDS<\/strong> The solids are similar. Find the missing measure(s).<br \/>\nQuestion 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30755\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-21.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 21\" width=\"202\" height=\"130\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere=2.5 cu. feet<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =5<br \/>\nv = 1.33 x 3.14\u00a0 x 5 x 5 x 5<br \/>\nv = 1.33 x 3.14 x 125<br \/>\nv = 1.33 x 392.5<br \/>\nv = 2.5 cu. feet<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30756\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-22.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 22\" width=\"239\" height=\"151\" \/><\/p>\n<p>Answer:<br \/>\nsurface area of triangular pyramid\u00a0 = 54 cubic m<\/p>\n<p>Explanation:<br \/>\nsurface area of triangular pyramid\u00a0 = area of faces + base<br \/>\narea of face 1 = 12<br \/>\narea of face 2 = 6<br \/>\narea of face 3 = 13<br \/>\narea of face 4 = 5<br \/>\narea of base = 18<br \/>\nA= 12 + 6 + 13 + 5 + 18<br \/>\nA = 18 + 13 + 23<br \/>\nA = 18 + 36<br \/>\nA = 54\u00a0 cubic m<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30757\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-23.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 23\" width=\"208\" height=\"130\" \/><\/p>\n<p>Answer:<br \/>\nvolume = 11.5 cu. mm<\/p>\n<p>Explanation:<br \/>\nvolume of triangular prism = (bhl\/2)<br \/>\nb = 4.6 , h = 4.6 , l = 6.4 given<br \/>\nv = (4.6 x 4.6 x 6.4\/2)<br \/>\nv = (21.16 x 6.4\/2)<br \/>\nv = (135.424\/2)<br \/>\nv = 11.5 cu. mm<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30758\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-24.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 24\" width=\"186\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cone = 8.0384 cu. in<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that\u00a0 r=1.6 ,h = 3<br \/>\nv = 3.14 x 1.6 x 1.6 x (3\/3)<br \/>\nv = 3.14 x 1.6\u00a0 x1.6\u00a0 x 1<br \/>\nv =3.14 x 2.56 x 1<br \/>\nv = 3.14 x 2.56<br \/>\nv = 8.0384 cu. in<\/p>\n<p><strong>FINDING SURFACE AREA<\/strong> The solids are similar. Find the surface area of the red solid. Round your answer to the nearest tenth if necessary.<br \/>\nQuestion 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30759\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-25.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 25\" width=\"237\" height=\"95\" \/><br \/>\nAnswer:<br \/>\nThe surface area of the red solid = 90 sq m<\/p>\n<p>Explanation:<br \/>\nGiven that the surface area of blue solid = 40 sq m<br \/>\ns0 the surface area of the red solid = 60 sq m<br \/>\n4\u00a0 x 10 = 40<br \/>\n9 x 10 = 90 sq m<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30760\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-26.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 26\" width=\"255\" height=\"117\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere= 14,094 cu. in<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =15<br \/>\nv = 1.33 x 3.14\u00a0 x 15 x 15 x 15<br \/>\nv = 1.33 x 3.14 x 3375<br \/>\nv = 1.33 x 10,597.5<br \/>\nv = 14,094.675 cu. in<\/p>\n<p>Question 17.<br \/>\n<strong>FINDING SURFACE AREA<\/strong><br \/>\nThe ratio of the corresponding linear measures of two similar cans is 4 to 7. The smaller can has a surface area of 220 square centimeters. Find the surface area of the larger can.<\/p>\n<p>Answer:<br \/>\nThe surface area of larger can = 55 sq cm<\/p>\n<p>Explanation:<br \/>\nGiven that the smaller can has a surface area of 220 sq cm<br \/>\nThe ratio of two similar cans is 4: 7<br \/>\n(220\/5) = 55 sq cm<\/p>\n<p><strong>FINDING VOLUME<\/strong> The solids are similar. Find the volume of the red solid.<br \/>\nQuestion 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30761\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-27.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 27\" width=\"243\" height=\"182\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of red soil =\u00a0 70 cu. mm<\/p>\n<p>Explanation:<br \/>\nsurface area of triangular pyramid\u00a0 = area of faces + base<br \/>\narea of face 1 = 21<br \/>\narea of face 2 = 21<br \/>\narea of face 3 = 7<br \/>\narea of face 4 = 7<br \/>\narea of base = 14<br \/>\nA= 21 + 21 + 7 + 7 + 14<br \/>\nA = 42 + 14 + 14<br \/>\nA = 42 + 28<br \/>\nA = 70 cu. mm<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30762\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-28.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 28\" width=\"204\" height=\"168\" \/><\/p>\n<p>Answer:<br \/>\nheight\u00a0 of cylinder=13,564.8 ft<\/p>\n<p>Explanation:<br \/>\nVolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14<br \/>\nr = 12<br \/>\nv = 3.14 x 12 x 12 x h<br \/>\n7850 = 3.14 x 144 h<br \/>\n7850= 452.16 h<br \/>\nh = (452.16\/7850)<br \/>\nh = 13,564.8 sq ft<\/p>\n<p>Question 20.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nThe ratio of the corresponding linear measures of two similar solids is 3:5. The volume of the smaller solid is 108 cubic inches. Your friend finds the volume of the larger solid. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30763\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-29.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 29\" width=\"238\" height=\"152\" \/><\/p>\n<p>Answer:<br \/>\nYes my friend is correct.<\/p>\n<p>Explanation:<br \/>\nthe volume of smaller solid is 108 cubic inches.<br \/>\n(108\/v) = (3\/5) x (3\/5)<br \/>\n(108\/v) = (9\/25)<br \/>\nv = 300 cubic in<\/p>\n<p>Question 21.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA hemisphere-shaped mole has a diameter of 5.7 millimeters and a surface area of about 51 square millimeters. The radius of the mole doubles. Estimate the new surface area of the mole.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30764\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-30.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 30\" width=\"132\" height=\"175\" \/><\/p>\n<p>Answer:<br \/>\nThe new surface area of the mole = 19.742 sq. mm<\/p>\n<p>Explanation:<br \/>\nsurface area of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nA = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r = 2.85<br \/>\nA = 1.33 x 3.14\u00a0 x 2.85 x 2.85<br \/>\nA= 1.33 x 3.14 x 8.1225<br \/>\nA = 1.33 x 25.50465<br \/>\nA = 19.742 sq. mm<\/p>\n<p>Question 22.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe volume of a 1968 Ford Mustang GT engine is 390 cubic inches. Which scale model of the Mustang has the greater engine volume, a 1 : 18 scale model or a 1 : 24 scale model? How much greater is it?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30765\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-31.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 31\" width=\"260\" height=\"135\" \/><br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou have a small marble statue of Wolfgang Mozart. It is 10 inches tall and weighs 16 pounds. The original marble statue is 7 feet tall.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30766\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-32.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 32\" width=\"199\" height=\"329\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-32.png 199w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-32-181x300.png 181w\" sizes=\"(max-width: 199px) 100vw, 199px\" \/><br \/>\na. Estimate the weight of the original statue. Explain your reasoning.<br \/>\nb. If the original statue were 20 feet tall, how much would it weigh?<\/p>\n<p>Answer:<br \/>\na. The weight of the original statue = 84\/10 cubic pounds<br \/>\nb. The original statue weight = 221 lb<\/p>\n<p>Explanation:<br \/>\na. The weight of the original statue = 7 ft<br \/>\n1 ft = 12 pounds<br \/>\n7 x 12 \/ 10 = 84\/10 cubic pounds.<br \/>\nb. given that the original statue was 20 ft<br \/>\n221,184 lb<\/p>\n<p>Question 24.<br \/>\n<strong>REPEATED REASONING<\/strong><br \/>\nThe nesting dolls are similar. The largest doll is 7 inches tall. Each of the other dolls is 1 inch shorter than the next larger doll. Make a table that compares the surface areas and the volumes of the seven dolls.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30767\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-33.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 33\" width=\"347\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-33.png 347w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-33-300x142.png 300w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36171\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Surface-Areas-and-Volumes-of-Similar-Solids-10.4-1.png\" alt=\"\" width=\"840\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Surface-Areas-and-Volumes-of-Similar-Solids-10.4-1.png 840w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Surface-Areas-and-Volumes-of-Similar-Solids-10.4-1-300x41.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Surface-Areas-and-Volumes-of-Similar-Solids-10.4-1-768x104.png 768w\" sizes=\"(max-width: 840px) 100vw, 840px\" \/><\/p>\n<p>Explanation:<br \/>\nIn the above given figure the larger doll is 7 inches tall.<br \/>\nEach of the other doll is 1 inch shorter than the next larger doll.<\/p>\n<p>Question 25.<br \/>\n<strong>PRECISION<\/strong><br \/>\nYou and a friend make paper cones to collect beach glass. You cut out the largest possible three-fourths circle from each piece of paper.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30768\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-34.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 10 Volume and Similar Solids 10.4 34\" width=\"479\" height=\"150\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-34.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-10-Volume-and-Similar-Solids-10.4-34-300x94.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\na. Are the cones similar? Explain your reasoning.<br \/>\nb. Your friend says that because your sheet of paper is twice as large, your cone will hold exactly twice the volume of beach glass. Is this true? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\na. Yes, the cones are similar.<br \/>\nb.No my friend is correct.<\/p>\n<p>Explanation:<br \/>\na. all circles are similar, the slant height and the circumference of the base of the cones are proportional .<br \/>\nb. my cone holds about 2 times as much my friend cone.<\/p>\n<h3><a id=\"Volume_and_Similar_Solids_Connecting_Concepts\"><\/a>Volume and Similar Solids Connecting Concepts<\/h3>\n<p><strong>Using the Problem-Solving Plan<\/strong><br \/>\nQuestion 1.<br \/>\nA yurt is a dwelling traditionally used in Mongolia and surrounding regions. The yurt shown is made of a cylinder and a cone. What is the volume of the yurt?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30772\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cc-1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cc 1\" width=\"237\" height=\"157\" \/><br \/>\nUnderstand the problem<br \/>\nYou know that the yurt is made of a cylinder and a cone. You also know several dimensions. You are asked to find the volume of the yurt.<br \/>\nMake a plan.<br \/>\nUse the Pythagorean Theorem to find the height of the cone. Then use the formulas for the volume of a cylinder and the volume of a cone to find the volume of the yurt.<br \/>\nSolve and check.<br \/>\nUse the plan to solve the problem. Then check your solution.<\/p>\n<p>Answer:<br \/>\nvolume of hurt = 4855 cu. ft<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that\u00a0 r = 15 ,h = 7<br \/>\nv = 3.14 x 15 x 15 x (17\/3)<br \/>\nv = 3.14 x 225\u00a0 x (17\/3)<br \/>\nv =3.14 x 225 x 5.666<br \/>\nv = 3.14 x 1275<br \/>\nv = 4,003<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 d =<br \/>\nr = 3 , h = 30<br \/>\nv = 3.14 x 3 x 3 x 30<br \/>\nv = 3.14 x 9 x 30<br \/>\nv= 3.14 x 270<br \/>\nh = 847.8<br \/>\n4008 +847 =4855<\/p>\n<p>Question 2.<br \/>\nsupervoidA spherical , a region in space that is unusually empty, has a diameter of 1.8 \u00d7 1<sup>9<\/sup> 0light-years. What is the volume of the supervoid? Use 3.14 for \u03c0. Write your answer in scientific notation.<\/p>\n<p>Answer:<br \/>\nvolume of supervoid =3.75858000000000 light years<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b3<br \/>\nv = (4\/3) x 3.14 x r\u00b3<br \/>\nv = 1.33 x 3.14 x 0.9<br \/>\nv = 2.826 x 1.33<br \/>\nv = 3.75858000000000 light years<\/p>\n<p>Question 3.<br \/>\nThe cylinders are similar. The volume of Cylinder A is \\(\\frac{8}{27}\\) times the volume of Cylinder B. Find the volume of each cylinder. Round your answers to the nearest tenth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30773\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cc-2.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cc 2\" width=\"244\" height=\"142\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cylinder = 452.16 cu. cm<\/p>\n<p>Explanation:<br \/>\nthe volume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14<br \/>\nr = 4 , h = 9<br \/>\nv = 3.14 x 4 x 4 x 9<br \/>\nv = 3.14 x 16 x 9<br \/>\nv= 3.14 x 144<br \/>\nh = 452.16 sq cm<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Packaging Salsa<br \/>\nAt the beginning of this chapter, you watched a STEAM Video called \u201cCanning Salsa.\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-30774\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cc-3.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cc 3\" width=\"365\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cc-3.png 365w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cc-3-300x145.png 300w\" sizes=\"(max-width: 365px) 100vw, 365px\" \/><\/p>\n<h3><a id=\"Volume_and_Similar_Solids_Chapter_Review\"><\/a>Volume and Similar Solids Chapter Review<\/h3>\n<p><strong>Review Vocabulary<\/strong><\/p>\n<p>Write the definition and give an example of each vocabulary term.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30775\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 1\" width=\"441\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-1.png 441w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-1-300x37.png 300w\" sizes=\"(max-width: 441px) 100vw, 441px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><\/p>\n<p>You can use a Summary Triangle to explain a concept. Here is an example of a Summary Triangle for volume of a cylinder.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30776\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-2.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 2\" width=\"376\" height=\"299\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-2.png 376w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-2-300x239.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/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-30777\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-3.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 3\" width=\"246\" height=\"323\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-3.png 246w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-3-228x300.png 228w\" sizes=\"(max-width: 246px) 100vw, 246px\" \/><br \/>\n1. volume of a cone<br \/>\n2. volume of a sphere<br \/>\n3. volume of a composite solid<br \/>\n4. surface areas of similar solids<br \/>\n5. volumes of similar solids<\/p>\n<p>Answer:<br \/>\ncone = A solid or hollow object which tapers from a circular or roughly circular base to a point.<br \/>\nhemisphere = a half of the celestial sphere as divided into two halves by the horizon.<br \/>\nsphere = a round solid figure, or its surface, with every point on its surface equidistant from its center.<br \/>\nsimilar solids = two solids are similar if they are the same type of solid and their corresponding radii, heights, base lengths, widths, etc. are proportional.<\/p>\n<p><strong>Chapter Self-Assessment<\/strong><\/p>\n<p>As 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-30778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-4.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 4\" width=\"593\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-4.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-4-300x39.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p><strong>10.1 Volumes of Cylinders (pp. 427\u2013432)<\/strong><br \/>\nLearning Target: Find the volume of a cylinder. Find the volume of the cylinder. Round your answer to the nearest tenth.<br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30779\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-5.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 5\" width=\"136\" height=\"96\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cylinder =1,236.375 cu. ft<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14\u00a0 d = 15 r = (d\/2)<br \/>\nr = 7.5 , h = 7 given<br \/>\nv = 3.14 x 7.5 x 7.5 x 7<br \/>\nv = 3.14 x 56.25 x 7<br \/>\nv = 3.14 x 393.75<br \/>\nv = 1,236.375 cu. ft<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30780\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-6.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 6\" width=\"127\" height=\"120\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cylinder =62.8 cu. cm<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14<br \/>\nr = 2 , h = 5 given<br \/>\nv = 3.14 x 2 x 2 x 5<br \/>\nv = 3.14 x 4 x 5<br \/>\nv = 3.14 x 20<br \/>\nv = 62.8 cu. cm<\/p>\n<p><strong>Find the missing dimension of the cylinder. Round your answer to the nearest whole number.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30781\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-7.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 7\" width=\"163\" height=\"178\" \/><\/p>\n<p>Answer:<br \/>\nheight of cylinder = 0.25232143 sq in<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14<br \/>\nr = 1.5 , v = 28 given<br \/>\n28 = 3.14 x 1.5 x 1.5 x h<br \/>\n28= 3.14 x 2.25h<br \/>\n28 = 7.065 h<br \/>\nh = 7.065\/28<br \/>\nh = 0.25232143 sq in<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30782\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-8.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 8\" width=\"160\" height=\"166\" \/><\/p>\n<p>Answer:<br \/>\nradius of cylinder =60.501 sq m<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14<br \/>\nh = 20 m, v = 7599 given<br \/>\n7599= 3.14 x r x r x 20<br \/>\n7599= 3.14 x 20 r\u00b2<br \/>\n7599 = 62.8 r\u00b2<br \/>\nr\u00b2 = 7599\/62.8<br \/>\nr\u00b2 = 121.00 m<br \/>\nr = 60.501 sq m<\/p>\n<p>Question 5.<br \/>\nYou are buying two cylindrical cans of juice. Each can holds the same amount of juice.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30783\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-9.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 9\" width=\"234\" height=\"237\" \/><br \/>\na. What is the height of Can B?<br \/>\nb. About how many cups of juice does 3\u2248each can hold? (1 in.<sup>3<\/sup> \u2248 0.07 cup)<\/p>\n<p>Answer:<br \/>\na.The height of can B = 0.074 in<br \/>\nb. The cups of juice does 3 each can hold = 21 cups<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14<br \/>\nh = 6, r = 3given<br \/>\nv = 3.14 x 3 x 3 x 6<br \/>\nv= 3.14 x 9 x 6<br \/>\nv = 3.14 x 54<br \/>\nv = 169.56 sq in<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14<br \/>\nv = 169.56, r = 2given<br \/>\n169.56 = 3.14 x 2 x 2 h<br \/>\n169.56= 3.14 x 4 h<br \/>\n169.56= 12.56 h<br \/>\nh = 0.074 in<br \/>\nb. 3 x 0.07<br \/>\n0.21<br \/>\n21 cups.<\/p>\n<p>Question 6.<br \/>\nYou triple the radius of a cylinder. How many times greater is the volume of the new cylinder? Explain.<\/p>\n<p>Answer:<br \/>\n3 times greater than the volume of the new cylinder.<\/p>\n<p>Explanation:<br \/>\nGiven that the radius is tripled.<br \/>\nvolume of cylinder = \u03c0r\u2075 h<\/p>\n<p><strong>10.2 Volumes of Cones (pp. 433\u2013438)<\/strong><br \/>\nLearning Target: Find the volume of a cone.<\/p>\n<p><strong>Find the volume of the cone. Round your answer to the nearest tenth.<\/strong><br \/>\nQuestion 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30784\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-10.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 10\" width=\"145\" height=\"100\" \/><\/p>\n<p>Answer:<\/p>\n<p>volume of\u00a0 cone= 803.84 cu. m<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 8 ,h = 12<br \/>\nv = 3.14 x 8 x 8 x (12\/3)<br \/>\nv = 3.14 x 64 x (12\/3)<br \/>\nv =3.14 x 64 x 4<br \/>\nv= 3.14 x 256<br \/>\nv = 803.84 cu. m<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30785\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-11.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 11\" width=\"199\" height=\"67\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone= 41.8666 cu. cm<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 2 ,h = 10<br \/>\nv = 3.14 x 2 x 2 x (10\/3)<br \/>\nv = 3.14 x 4 x (10\/3)<br \/>\nv =3.14 x 4 x 3.33<br \/>\nv= 3.14 x 13.33<br \/>\nv = 41.8666 cu. cm<\/p>\n<p><strong>Find the missing dimension of the cone. Round your answer to the nearest tenth.<\/strong><br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30787\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-12.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 12\" width=\"168\" height=\"101\" \/><\/p>\n<p>Answer:<br \/>\nradius of\u00a0 cone= 0.006173\u00a0 in<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that ,h = 36<br \/>\n3052= 3.14 x r x r (36\/3)<br \/>\n3052 = 3.14 x 12 r\u00b2<br \/>\n3052 =37.68 r\u00b2<br \/>\nr\u00b2= 0.012346<br \/>\nv = 0.006173 cu. in<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30788\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-13.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 13\" width=\"130\" height=\"170\" \/><\/p>\n<p>Answer:<br \/>\nheight of\u00a0 cone=0.041866 sq mm<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that ,r =6<br \/>\n900= 3.14 x 6 x 6 (h\/3)<br \/>\n900 = 3.14 x 12 h<br \/>\n900 =37.68 h<br \/>\nh= (37.68\/900)<br \/>\nh\u00a0 = 0.041866 sq mm<\/p>\n<p>Question 11.<br \/>\nThe paper cup can hold 84.78 cubic centimeters of water. What is the height of the cup?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30790\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-14.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 14\" width=\"114\" height=\"107\" \/><\/p>\n<p>Answer:<br \/>\nheight of\u00a0 cone= \u00a00.111111 cm<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that ,r =3<br \/>\n84.78= 3.14 x 3 x 3 (h\/3)<br \/>\n84.78 = 3.14 x 3 h<br \/>\n84.78 =9.42 h<br \/>\nh= (9.42\/84.78)<br \/>\nh\u00a0 = 0.111111 cm<\/p>\n<p><strong>10.3 Volumes of Spheres (pp. 439\u2013444)<\/strong><br \/>\nLearning Target: Find the volume of a sphere.<\/p>\n<p><strong>Find the volume of the sphere. Round your answer to the nearest tenth.<\/strong><br \/>\nQuestion 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30791\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-15.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 15\" width=\"123\" height=\"117\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere=7,216.4736 cubic ft<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =12<br \/>\nv = 1.33 x 12\u00a0 x 12 x 12 x 3.14<br \/>\nv = 1.33 x 3.14 x 1728<br \/>\nv = 1.33 x 5,425.92<br \/>\nv = 7,216.4736 cubic ft<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30792\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-16.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 16\" width=\"120\" height=\"116\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere= 5,558.52222 cu. cm<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =11<br \/>\nv = 1.33 x 11\u00a0 x 11 x 11 x 3.14<br \/>\nv = 1.33 x 3.14 x 1331<br \/>\nv = 1.33 x 4,179.34<br \/>\nv = 5,558.52222 cu. cm<\/p>\n<p>Question 14.<br \/>\nThe volume of a water walking ball is \\(\\frac{4}{3}\\)\u03c0 cubic meters. Find the diameter of the water walking ball.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30793\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-17.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 17\" width=\"207\" height=\"150\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Find the volume of the composite solid. Round your answer to the nearest tenth if necessary.<\/strong><br \/>\nQuestion 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30795\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-18.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 18\" width=\"129\" height=\"157\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone=\u00a0 452.16 cu. m<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that ,r = 6, h = 12<br \/>\nv= 3.14 x 6 x 6 (12\/3)<br \/>\nv = 3.14 x 36 x (12\/3)<br \/>\nv =3.14 x 36 x 4<br \/>\nv= 3.14 x 144<br \/>\nv\u00a0 = 452.16 cu. m<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30797\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-19.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 19\" width=\"127\" height=\"115\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of solid=\u00a0 31 cu. ft<\/p>\n<p>Explanation:<br \/>\nsurface area of triangular pyramid\u00a0 = area of faces + base<br \/>\narea of face 1 = 6<br \/>\narea of face 2 = 6<br \/>\narea of face 3 = 2<br \/>\narea of face 4 = 5<br \/>\narea of base = 12<br \/>\nA= 6 + 6 + 2 + 5 + 12<br \/>\nA = 12 + 7 + 12<br \/>\nA = 24 + 7<br \/>\nA = 31\u00a0 \u00a0sq ft<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30800\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-20.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 20.1\" width=\"135\" height=\"135\" \/><\/p>\n<p>Answer:<br \/>\nvolume of cylinder =50.24 cu. cm<\/p>\n<p>Explanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14<br \/>\nr = 2 , h = 4 given<br \/>\nv = 3.14 x 2 x 2 x 4<br \/>\nv = 3.14 x 16<br \/>\nv= 50.24 cu. cm<\/p>\n<p>Question 18.<br \/>\nThe volume of water that a submerged object displaces is equal to the volume of the object. Find the radius of the sphere. Round your answer to the nearest tenth.(1 mL = 1 cm<sup>3<\/sup>)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30801\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-20.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 20\" width=\"241\" height=\"156\" \/><br \/>\nAnswer:<\/p>\n<p><strong>10.4 Surface Areas and Volumes of Similar Solids (pp. 445\u2013452)<\/strong><br \/>\nLearning Target: Find the surface areas and volumes of similar solids.<\/p>\n<p>Question 19.<br \/>\nDetermine whether the solids are similar.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30802\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-21.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 21\" width=\"227\" height=\"123\" \/><\/p>\n<p>Answer:<br \/>\nVolume of cylinder= 0.17840909 cu. cm<\/p>\n<p>Explanation:<br \/>\nVolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14<br \/>\nr = 2.5<br \/>\n110 = 3.14 x 2.5 x 2.5 x h<br \/>\n110 = 3.14 x 6.25 h<br \/>\n110= 19.625 h<br \/>\nh = (19.625\/110)<br \/>\nh = 0.17840909 sq cm<\/p>\n<p>Question 20<br \/>\nThe prisms are similar. Find the missing measures.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30803\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-22.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 22\" width=\"311\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-22.png 311w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-22-300x108.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><\/p>\n<p>Answer:<\/p>\n<p>Question 21.<br \/>\nThe prisms are similar. Find the surface area of the red prism. Round your answer to the nearest tenth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30804\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-23.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 23\" width=\"237\" height=\"129\" \/><br \/>\nAnswer:<br \/>\nvolume = 67.712 cubic cm<\/p>\n<p>Explanation:<br \/>\nvolume of triangular prism = (bhl\/2)<br \/>\nb = 4.6 , h = 4.6 , l = 6.4 given<br \/>\nv = (4.6 x 4.6 x 6.4\/2)<br \/>\nv = (21.16 x 6.4\/2)<br \/>\nv = (135.424\/2)<br \/>\nv = 67.712 cubic\u00a0 cm<\/p>\n<p>Question 22.<br \/>\nThe pyramids are similar. Find the volume of the red pyramid.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30805\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-10-Volume-and-Similar-Solids-cr-24.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 10 Volume and Similar Solids cr 24\" width=\"236\" height=\"126\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of red soil =\u00a0 70 cu. mm<\/p>\n<p>Explanation:<br \/>\nsurface area of triangular pyramid\u00a0 = area of faces + base<br \/>\narea of face 1 = 21<br \/>\narea of face 2 = 21<br \/>\narea of face 3 = 7<br \/>\narea of face 4 = 7<br \/>\narea of base = 14<br \/>\nA= 21 + 21 + 7 + 7 + 14<br \/>\nA = 42 + 14 + 14<br \/>\nA = 42 + 28<br \/>\nA = 70\u00a0 sqmm<\/p>\n<p>Question 23.<br \/>\nThe ratio of the corresponding linear measures of two similar jewelry boxes is 2 to 3. The larger jewelry box has a volume of 162 cubic inches. Find the volume of the smaller jewelry box.<\/p>\n<p>Answer:<br \/>\nvolume of the jewelry box = 36.4 cubics in<\/p>\n<p>Explanation:<br \/>\ngiven that 2: 3 ratio<br \/>\n(162\/v) = (2\/3) x (2\/3)<br \/>\n(162\/v) = (4\/9)<br \/>\n4v = 1458<br \/>\nv = (1458\/4)<br \/>\nv = 36.4 cubic in<\/p>\n<h3><a id=\"Volume_and_Similar_Solids_Practice_Test\"><\/a>Volume and Similar Solids Practice Test<\/h3>\n<p><strong>Find the volume of the solid. Round your answer to the nearest tenth.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30807\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-pt-1.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids pt 1\" width=\"137\" height=\"112\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere=33,409.6 cu. mm<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =20<br \/>\nv = 1.33 x 20 x 20 x 20 x 3.14<br \/>\nv = 1.33 x 3.14 x 8000<br \/>\nv = 1.33 x 25,120<br \/>\nv = 33,409.6 cu. mm<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30809\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-pt-2.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids pt 2\" width=\"91\" height=\"123\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone=\u00a0 452.16 cu. m<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that ,r = 6, h = 12<br \/>\nv= 3.14 x 6 x 6 (12\/3)<br \/>\nv = 3.14 x 36 x (12\/3)<br \/>\nv =3.14 x 36 x 4<br \/>\nv= 3.14 x 144<br \/>\nv\u00a0 = 452.16 cu. m<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30812\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-pt-3.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids pt 3\" width=\"126\" height=\"116\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the sphere=33,409.6 cu. mm<\/p>\n<p>Explanation:<br \/>\nvolume of sphere = (4\/3) \u03c0r\u00b2 x r<br \/>\nv\u00a0 = (4\/3) x 3.14 x r\u00b3<br \/>\nwhere r =20<br \/>\nv = 1.33 x 20 x 20 x 20 x 3.14<br \/>\nv = 1.33 x 3.14 x 8000<br \/>\nv = 1.33 x 25,120<br \/>\nv = 33,409.6 cu. mm<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30813\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-pt-4.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids pt 4\" width=\"149\" height=\"138\" \/><br \/>\nAnswer:<br \/>\nvolume of\u00a0 cone=\u00a0 452.16 cu. m<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that ,r = 6, h = 12<br \/>\nv= 3.14 x 6 x 6 (12\/3)<br \/>\nv = 3.14 x 36 x (12\/3)<br \/>\nv =3.14 x 36 x 4<br \/>\nv= 3.14 x 144<br \/>\nv\u00a0 = 452.16 cu. m<\/p>\n<p>Question 5.<br \/>\nThe pyramids are similar.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30814\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-pt-5.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids pt 5\" width=\"350\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-pt-5.png 350w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-pt-5-300x113.png 300w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><br \/>\na. Find the missing measures.<br \/>\nb. Find the surface area of the red pyramid.<\/p>\n<p>Answer:<br \/>\nThe volume of red soil =\u00a0 70 cu. mm<\/p>\n<p>Explanation:<br \/>\nsurface area of triangular pyramid\u00a0 = area of faces + base<br \/>\narea of face 1 = 21<br \/>\narea of face 2 = 21<br \/>\narea of face 3 = 7<br \/>\narea of face 4 = 7<br \/>\narea of base = 14<br \/>\nA= 21 + 21 + 7 + 7 + 14<br \/>\nA = 42 + 14 + 14<br \/>\nA = 42 + 28<\/p>\n<p>Question 6.<br \/>\nYou are making smoothies. You will use either the cone-shaped glass or the cylindrical glass. Which glass holds more? About how much more?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-pt-6.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids pt 6\" width=\"224\" height=\"131\" \/><br \/>\nAnswer:<br \/>\nvolume of\u00a0 cone=\u00a0 452.16 cu. m<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that ,r = 6, h = 12<br \/>\nv= 3.14 x 6 x 6 (12\/3)<br \/>\nv = 3.14 x 36 x (12\/3)<br \/>\nv =3.14 x 36 x 4<br \/>\nv= 3.14 x 144<br \/>\nv\u00a0 = 452.16 cu. m<\/p>\n<p>Question 7.<br \/>\nThe ratio of the corresponding linear measures of two similar waffle cones is 3 to 4. The smaller cone has a volume of about 18 cubic inches. Find the volume of the larger cone. Round your answer to the nearest tenth.<\/p>\n<p>Answer: 24 cubic inches.<\/p>\n<p>Explanation:<br \/>\n(18\/v) = (3\/4)<br \/>\n3v = 18 x 4<br \/>\n3v = 72<br \/>\nv = 24 cubic in<\/p>\n<p>Question 8.<br \/>\nDraw two different composite solids that have the same volume but different surface areas.Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nThere are 13.5\u03c0 cubic inches of blue sand and 9\u03c0 cubic inches of red sand in the cylindrical container. How many cubic inches of white sand are in the container? Round your answer to the nearest tenth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-pt-9.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids pt 9\" width=\"149\" height=\"173\" \/><br \/>\nAnswer:<br \/>\nv = 169.56 cu. in<br \/>\nExplanation:<br \/>\nvolume of cylinder = \u03c0r\u00b2 h<br \/>\nwhere \u03c0 = 3.14<br \/>\nh = 6, r = 3given<br \/>\nv = 3.14 x 3 x 3 x 6<br \/>\nv= 3.14 x 9 x 6<br \/>\nv = 3.14 x 54<br \/>\nv = 169.56 cu. in<\/p>\n<p>Question 10.<br \/>\nWithout calculating, determine which solid has the greater volume. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30820\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-10-Volume-and-Similar-Solids-pt-10.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 10 Volume and Similar Solids pt 10\" width=\"254\" height=\"123\" \/><\/p>\n<p>Answer:<br \/>\nprism has great volume.<\/p>\n<p>Explanation:<br \/>\nthe volume of the sphere is less than the volume of a prism.<\/p>\n<h3><a id=\"Volume_and_Similar_Solids_Cumulative_Practice\"><\/a>Volume and Similar Solids Cumulative Practice<\/h3>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-30821\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids cp 1\" width=\"307\" height=\"347\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-1.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-1-265x300.png 265w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\nQuestion 1.<br \/>\nWhat is the value of 14 &#8211; 2\\(\\sqrt [ 3 ]{ 64 } \\) ?<br \/>\nA. &#8211; 50<br \/>\nB. &#8211; 2<br \/>\nC. 6<br \/>\nD. 48<br \/>\nAnswer:<br \/>\noption A Is correct<\/p>\n<p>Explanation:<br \/>\n14 &#8211; 2 (3\/64 x 100)<br \/>\n12 (150\/32)<br \/>\n12 x (75\/16)<br \/>\n-50<\/p>\n<p>Question 2.<br \/>\nWhat is the volume of the cone? (Use \\(\\frac{22}{7}\\) for \u03c0.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30822\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-2.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids cp 2\" width=\"412\" height=\"226\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-2.png 412w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-2-300x165.png 300w\" sizes=\"(max-width: 412px) 100vw, 412px\" \/><\/p>\n<p>Answer:<br \/>\nvolume of\u00a0 cone=\u00a0 4098. 8304 cubic cm<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cone\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that ,r = 14, h = 20<br \/>\nv= 3.14 x 14 x 14 (20\/3)<br \/>\nv = 3.14 x196 x (20\/3)<br \/>\nv =3.14 x 196 x 6.66<br \/>\nv= 3.14 x 1305.36<br \/>\nv\u00a0 = 4098. 8304<\/p>\n<p>Question 3.<br \/>\nThe cylinders are similar. What is the volume of the red cylinder?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-3.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids cp 3\" width=\"311\" height=\"163\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-3.png 311w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-3-300x157.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><br \/>\nA. 6 cm<br \/>\nB. 150.75 cm<sup>3<\/sup><br \/>\nC. 301.5 cm<sup>3<\/sup><br \/>\nD. 603 cm<sup>3<\/sup><\/p>\n<p>Answer:<br \/>\noption D is correct.<\/p>\n<p>Explanation:<br \/>\n(1206\/2 ) = 603<br \/>\nlarge cylinder is 2 times greater than small cylinder.<\/p>\n<p>Question 4.<br \/>\nA rectangle is graphed in the coordinate plane.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-4.1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids cp 4.1\" width=\"184\" height=\"142\" \/><br \/>\nWhich of the following shows Rectangle E&#8217;F&#8217;G&#8217;H&#8217;, the image of Rectangle EFGH after it is reflected in the -axis?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-4.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids cp 4\" width=\"501\" height=\"294\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-4.png 501w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-4-300x176.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><\/p>\n<p>Answer:<br \/>\noption\u00a0 I is correct.<\/p>\n<p>Explanation:<br \/>\nEFGH\u00a0 is reflected in the -ve axis.<\/p>\n<p>Question 5.<br \/>\nWhat are the ordered pairs shown in the mapping diagram?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-5.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids cp 5\" width=\"153\" height=\"141\" \/><br \/>\nA. (2, 5), (4, &#8211; 2), (6, &#8211; 7), (8, 1)<br \/>\nB. (2, &#8211; 7), (4, &#8211; 2), (6, 1), (8, 5)<br \/>\nC. (2, 5), (4, 1), (6, &#8211; 2), (8, &#8211; 7)<br \/>\nD. (5, 2), (- 2, 4), (- 7, 6), (1, 8)<\/p>\n<p>Answer:<br \/>\noption A is correct.<\/p>\n<p>Explanation:<br \/>\n(2, 5)<br \/>\n(4, -2)<br \/>\n(6, -7)<br \/>\n(8, 1)<\/p>\n<p>Question 6.<br \/>\nWhat is \\(0 . \\overline{75}\\) written as a fraction?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-6.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids cp 6\" width=\"90\" height=\"61\" \/><\/p>\n<p>Answer:<\/p>\n<p>Question 7.<br \/>\nSolve the formula A = P + PI for I.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30838\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-7.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids cp 7\" width=\"431\" height=\"98\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-7.png 431w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-7-300x68.png 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><\/p>\n<p>Answer:<br \/>\noption I is correct.<\/p>\n<p>Explanation:<br \/>\nA = P + PI<br \/>\nI = (A &#8211; P\/P)<br \/>\nA = P + P (A &#8211; P\/P)<br \/>\nA = A.<\/p>\n<p>Question 8.<br \/>\nA cylinder has a volume of 1296 cubic inches. If you divide the radius of the cylinder by 12, what is the volume (in cubic inches) of the smaller cylinder?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-6.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids cp 6\" width=\"90\" height=\"61\" \/><\/p>\n<p>Answer:<br \/>\nThe volume =0.1162963 cubic in<\/p>\n<p>Explanation:<br \/>\nvolume of\u00a0 cylinder\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 12 , v = 1296<br \/>\n1296 = 3.14 x 12 x 12 x (h\/3)<br \/>\n1296 = 3.14 x 12x 4h<br \/>\n1296 =3.14 x\u00a0 48 h<br \/>\n1296= 150.72 h<br \/>\nh =(150.72\/1296)<br \/>\nh = 0.1162963 cubic in<\/p>\n<p>Question 9.<br \/>\nThe cost y (in dollars) for pounds of grapes is represented by y = 2x. Which graph represents the equation?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-9.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids cp 9\" width=\"562\" height=\"497\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-9.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-9-300x265.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Answer:<br \/>\nOption c is correct.<\/p>\n<p>Explanation:<br \/>\ny = 2x<br \/>\non the x axis the graph represents the straight line on x &#8211; axis.<\/p>\n<p>Question 10.<br \/>\nYou are making a giant crayon. What is the volume (in cubic centimeters) of the entire crayon? Show your work and explain your reasoning. (Use 3.14 for \u03c0.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-30840\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-10.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids cp 10\" width=\"304\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-10.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10-Volume-and-Similar-Solids-cp-10-300x80.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\nAnswer:<br \/>\nThe volume = =75.34116 cubic cm<\/p>\n<p>Explanation:<br \/>\nthe volume of\u00a0 cylinder\u00a0 =\u03c0r\u00b2 (h\/3)<br \/>\ngiven that r = 3 ,h = 8<br \/>\nv = 3.14 x 3 x 3 x (8\/3)<br \/>\nv = 3.14 x 9 x (8\/3)<br \/>\nv =3.14 x 9 x 2.666<br \/>\nv= 3.14 x 23.994<br \/>\nv = 75.34116 cubic cm<\/p>\n<h3>Conclusion<\/h3>\n<p>We wish the knowledge shared regarding the Big Ideas Math Answers Grade 8 Ch 10 Volume and Similar Solids has helped you in your preparation. In case of any queries, do leave us your suggestions via the comment section and we will get back to you.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Big Ideas Math Answers 8th Grade Ch 10 Volume and Similar Solids helps you to have strong fundamentals of concepts underlying. Learn the associated lessons of Volume and Similar Solids easily and quickly taking the help of the BIM Book Grade 8 Chapter 10 Answers. All the Big Ideas Math Grade 8 Answers Chapter 10 &#8230; <a title=\"Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-8-chapter-10\/\" aria-label=\"More on Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids\">Read more<\/a><\/p>\n","protected":false},"author":12,"featured_media":89324,"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\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-10.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/30601"}],"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=30601"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/30601\/revisions"}],"predecessor-version":[{"id":90324,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/30601\/revisions\/90324"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89324"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=30601"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=30601"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=30601"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}