{"id":14907,"date":"2022-04-02T10:30:23","date_gmt":"2022-04-02T05:00:23","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=14907"},"modified":"2022-04-07T11:06:19","modified_gmt":"2022-04-07T05:36:19","slug":"big-ideas-math-answers-grade-5-chapter-13","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-5-chapter-13\/","title":{"rendered":"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume"},"content":{"rendered":"<p>A perfect preparation will come to your hand when you have the best source with you. Finding the best source will help you to save your time while preparing and also get a grip on the concept. The only best source to learn all the Grade 5 Chapter 13 Understand Volume is our <strong><a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-5\/\">Big Ideas Math Answers Grade 5<\/a> Chapter 13 Understand Volume<\/strong>. Why every student love to use our Big Ideas Math Answers 5th Grade Answer Key Chapter 13 Understand Volume? Do you want to know why? Because we have provided from basic concepts to difficult concepts.<\/p>\n<h2>Big Ideas Math Book 5th Grade Chapter 13 Understand Volume Answer Key<\/h2>\n<p>We are providing different methods to solve problems, practice tests, quiz, objective question and answers, ad a detailed explanation for problems, etc. Get a<strong> free pdf of Big Ideas Math Answer Key Grade 5th<\/strong>. Good practice will help you to score the best marks in the exam. Therefore, without wasting your time, quickly start your preparation now. We have given quick links along with various problems. Try to practice all problems and become a pro in your math subject.<\/p>\n<p><strong>Lesson: 1 Understand the Concept of Volume<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_13.1_Understand_the_Concept_of_Volume\">Lesson 13.1 Understand the Concept of Volume<\/a><\/li>\n<li><a href=\"#Understand_the_Concept_of_Volume_Homework_&amp;_Practice_13.1\">Understand the Concept of Volume Homework &amp; Practice 13.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Find Volumes of Right Rectangular Prisms<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_13.2_Find_Volumes_of_Right_Rectangular_Prisms\">Lesson 13.2 Find Volumes of Right Rectangular Prisms<\/a><\/li>\n<li><a href=\"#Find_Volumes_of_Right_Rectangular_Prisms_Homework_&amp;_Practice_13.2\">Find Volumes of Right Rectangular Prisms Homework &amp; Practice 13.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Apply the Volume Formula<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_13.3_Apply_the_Volume_Formula\">Lesson 13.3 Apply the Volume Formula<\/a><\/li>\n<li><a href=\"#Apply_the_Volume_Formula_Homework_&amp;_Practice_13.3\">Apply the Volume Formula Homework &amp; Practice 13.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Find Unknown Dimensions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_13.4_Find_Unknown_Dimensions\">Lesson 13.4 Find Unknown Dimensions<\/a><\/li>\n<li><a href=\"#Find_Unknown_Dimensions_Homework_&amp;_Practice_13.4\">Find Unknown Dimensions Homework &amp; Practice 13.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Find Volumes of Composite Figures<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_13.5_Find_Volumes_of_Composite_Figures\">Lesson 13.5 Find Volumes of Composite Figures<\/a><\/li>\n<li><a href=\"#Find_Volumes_of_Composite_Figures_Homework_&amp;_Practice_13.5\">Find Volumes of Composite Figures Homework &amp; Practice 13.5<\/a><\/li>\n<\/ul>\n<p><strong>Chapter: 13 &#8211; Understand Volume<\/strong><\/p>\n<ul>\n<li><a href=\"#Understand_Volume_Performance_Task_13\">Understand Volume Performance Task 13<\/a><\/li>\n<li><a href=\"#Understand_Volume_Activity\">Understand Volume Activity<\/a><\/li>\n<li><a href=\"#Understand_Volume_Chapter_Practice\">Understand Volume Chapter Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Lesson_13.1_Understand_the_Concept_of_Volume\"><\/a>Lesson 13.1 Understand the Concept of Volume<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Use centimeter cubes to make each figure.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14972\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-1.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 1\" width=\"525\" height=\"359\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-1.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-1-300x205.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Which figure takes up the most space? Which figure takes up the least space? How do you know?<\/p>\n<p>Answer:<br \/>\nFigure-3 occupies more space.<\/p>\n<p>Explanation:<br \/>\nfigure-1<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 9 x 9 x 1<br \/>\nIn the above-given figure l=9 ft, w =9 ft and h = 1ft<br \/>\nvolume = 9 x 9 x 1<br \/>\nvolume = 81x 1<br \/>\nvolume = 81 cubic ft<br \/>\nfigure-2<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 3 x 3 x 2<br \/>\nIn the above-given figure l=3 ft, w =3 ft and h = 2 ft<br \/>\nvolume = 3 x 3 x 2<br \/>\nvolume = 9 x 2<br \/>\nvolume = 18 cubic ft<br \/>\nfigure-3<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 7 x 3 x 5<br \/>\nIn the above-given figure l=7 ft, w =3 ft and h = 5 ft<br \/>\nvolume = 7 x 3 x 5<br \/>\nvolume = 21 x 5<br \/>\nvolume = 105 cubic ft<br \/>\nfigure-4<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 3 x 3 x 1<br \/>\nIn the above-given figure l=3 ft, w =3 ft and h = 1 ft<br \/>\nvolume = 3 x 3 x 1<br \/>\nvolume = 9 x 1<br \/>\nvolume = 9 cubic ft<\/p>\n<p><strong>Structure<\/strong><br \/>\nCan two different figures take up the same amount of space? Explain.<\/p>\n<p>Answer:<br \/>\nYes.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14974\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-3.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 3\" width=\"190\" height=\"126\" \/><br \/>\nIn example\u00a0 1 :if we consider l= 3 cm and w = 2 cm and h = 2cm<br \/>\nv = l x w x h<br \/>\nvolume = length x width x height<br \/>\nv = 3 x 2 x 2<br \/>\nv = 6 x 2<br \/>\nv = 12 cubic cm<br \/>\nIn example 2 : if we consider l= 2 cm and w = 3 cm and h = 2cm.<br \/>\nv = l x w x h<br \/>\nvolume = length x width x height<br \/>\nv = 2 x 3 x 2<br \/>\nv = 6 x 2<br \/>\nv = 12\u00a0 cubic cm.<br \/>\nboth the volumes are same.<\/p>\n<p><strong>Think and Grow: Use Unit Cubes to Find Volume<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nVolume is a measure of the amount of space that a solid figure occupies. The volume of a unit cube is 1 cubic unit. You can count unit cubes to find the volume of a solid figure.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14973\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-2.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 2\" width=\"506\" height=\"314\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-2.png 506w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-2-300x186.png 300w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><br \/>\n<strong>Example<\/strong><br \/>\nFind the volume of the figure.<br \/>\nThe figure is made of __ unit cubes.<br \/>\nSo, the volume of the figure is _1_ cubic units.<\/p>\n<p>Answer:<br \/>\nThe volume of the figure = 12 cubic feet.<br \/>\nThe figure is made up of 7 unit cubes.<br \/>\nSo, the volume of the figure is 1 cubic units.<\/p>\n<p>Explanation:<br \/>\nThe volume of the figure = l x w x h<br \/>\nwhere l = length, w = width and h = height.<br \/>\ngiven that l = 4 , w= 3 and h = 1<br \/>\nv = 4 x 3 x 1<br \/>\nv = 12 x 1<br \/>\nv = 12 cubic feet.<br \/>\nThe figure is made up of 7 unit cubes.<br \/>\nSo, the volume of the figure is 1 cubic units.<\/p>\n<p><strong>Example<\/strong><br \/>\nFind the volume of the figure.<br \/>\nEach unit cube has an edge length of ___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14974\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-3.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 3\" width=\"190\" height=\"126\" \/><br \/>\nSo, each unit cube has a volume of ___.<br \/>\nThe figure is made of ___ unit cubes.<br \/>\nSo, the volume of the figure is ___.<\/p>\n<p>Answer:<br \/>\nEach cube has an edge length of 1 unit<br \/>\nSo, each cube has a volume of 1 cubic unit.<br \/>\nThe figure is made of 12 unit cubes.<br \/>\nSo, the volume of the figure is 12 cubic cm<\/p>\n<p>Explanation:<br \/>\nEach cube has an edge length of 1 unit<br \/>\nSo, each cube has a volume of 1 cubic unit.<br \/>\nv = l x w x h<br \/>\nv = 1 x 1 x 1<br \/>\nv = 1 cubic unit<br \/>\nvolume of figure = l x w x h<br \/>\nv = 3 x 2 x 2<br \/>\nwhere l = 3 cm , w = 2 cm and h = 2 cm given.<br \/>\nv = 3 x 2 x 2<br \/>\nv = 6 x 2<br \/>\nv = 12 cubic cm.<br \/>\n<strong>Show and Grow<\/strong><\/p>\n<p>Find the volume of the figure.<\/p>\n<p>Question 1.<br \/>\nVolume = 6 cubic units<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14975\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-4.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 4\" width=\"152\" height=\"149\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the cube = 16 cubic feet.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 4 x 1 x 4<br \/>\nIn the above-given figure l=4 ft, w =1 ft and h = 4ft<br \/>\nvolume = 4 x 1 x 4<br \/>\nvolume = 4 x 4<br \/>\nvolume = 16 cubic ft<\/p>\n<p>Question 2.<br \/>\nVolume <span style=\"font-size: 16px;\">= ___<br \/>\n<\/span><span style=\"font-size: 16px; font-style: normal; font-weight: 400;\">Answer :- 16<\/span><br \/>\n<span style=\"font-size: 16px; font-style: normal; font-weight: 400;\">Explanat<\/span><span style=\"font-size: 16px; font-style: normal; font-weight: 400;\">ion:-\u00a0 width*length*height(w*l*h)<\/span><br \/>\n= 2*4*2<br \/>\n=16<br \/>\n<img loading=\"lazy\" class=\"size-full wp-image-14976 alignleft\" style=\"font-weight: inherit;\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-5.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 5\" width=\"164\" height=\"143\" \/><span style=\"font-size: 16px;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>Answer:<br \/>\nThe volume of cube = 16 cubic feet.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 4 x 2 x 2<br \/>\nIn the above-given figure l=4 ft, w = 2 ft and h = 2ft<br \/>\nvolume = 4 x 2 x 2<br \/>\nvolume = 8 x 12<br \/>\nvolume = 16 cubic ft<\/p>\n<p><strong>Apply and \u00a0Grow: Practice<\/strong><\/p>\n<p>Find the volume of the figure.<\/p>\n<p>Question 3.<br \/>\nVolume = ___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14977\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-6.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 6\" width=\"96\" height=\"143\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the figure = 9 cubic feet.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 3 x 1 x 3<br \/>\nIn the above-given figure l=3 ft, w = 1 ft and h = 3ft<br \/>\nvolume = 3 x 3<br \/>\nvolume = 9 cubic ft<\/p>\n<p>Question 4.<br \/>\nVolume = ___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14978\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-7.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 7\" width=\"130\" height=\"109\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the figure = 18 cubic feet.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 3 x 3 x 2<br \/>\nIn the above-given figure l=3 ft, w = 3 ft and h = 2ft<br \/>\nvolume = 3 x 3 x 2<br \/>\nvolume = 9 x 2<br \/>\nvolume = 18 cubic feet<\/p>\n<p>Question 5.<br \/>\nVolume = ____<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15013\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-8.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 8\" width=\"170\" height=\"100\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the figure = 9 cubic feet.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 3 x 1 x 3<br \/>\nIn the above-given figure l=3 ft, w = 1 ft and h = 3 ft<br \/>\nvolume = 3 x 1 x 3<br \/>\nvolume = 3 x 3<br \/>\nvolume = 9 cubic feet<\/p>\n<p>Question 6.<br \/>\nVolume = ____<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15014\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-9.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 9\" width=\"240\" height=\"146\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the figure = 40 cubic feet.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 4 x 2 x 5<br \/>\nIn the above-given figure l=4 ft, w = 2 ft and h = 5 ft<br \/>\nvolume = 4 x 2 x 5<br \/>\nvolume = 8 x 5<br \/>\nvolume = 40 cubic feet<\/p>\n<p>Question 7.<br \/>\nCube-shaped shipping boxes, like the one shown, are packed into a van. They form a solid without any gaps or overlaps that is 3 feet long, 2 feet wide, and 3 feet tall. What is the volume of the solid formed?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15015\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-10.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 10\" width=\"81\" height=\"87\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the solid formed = 40 cubic feet.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 3 x 2 x 3<br \/>\nIn the above-given figure l=3 ft, w = 2 ft and h = 3 ft<br \/>\nvolume = 3 x 2 x 3<br \/>\nvolume = 6 x 3<br \/>\nvolume = 18 cubic feet<\/p>\n<p>Question 8.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend says the volume of the figure is 12 cubic centimeters. Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15016\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-11.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 11\" width=\"219\" height=\"128\" \/><\/p>\n<p>Answer:<br \/>\nNo my friend is not correct.<br \/>\nThe volume of the figure = 24 cubic cm.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 4 x 2 x 3<br \/>\nIn the above-given figure l=4 ft, w = 2 ft and h = 3 ft<br \/>\nvolume = 4 x 2 x 3<br \/>\nvolume = 8 x 3<br \/>\nvolume = 24 cubic feet<\/p>\n<p>Question 9.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWhat is the volume of the figure formed by the missing cubes?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15017\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-12.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 12\" width=\"202\" height=\"180\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the figure formed by the missing cubes = 32 cubic inches.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 4 x 4 x 2<br \/>\nIn the above-given figure l=4 ft, w = 4 ft and h = 2 ft<br \/>\nvolume = 4 x 4 x 2<br \/>\nvolume = 16 x 2<br \/>\nvolume = 32 cubic feet<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nThe puzzle is made of unit cubes. A box can hold 20 of the puzzles without any gaps or overlaps. What is the volume of the box?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15018\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-13.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 13\" width=\"147\" height=\"146\" \/><br \/>\nFind the volume of one puzzle.<br \/>\nThe puzzle is made of unit cubes that each have an edge length of ___.<br \/>\nSo, each unit cube has a volume of ___.<br \/>\nOne puzzle is made of ___ unit cubes.<br \/>\nSo, the volume of one puzzle is ___.<\/p>\n<p>Answer:<br \/>\nThe puzzle is made of unit cubes that each have an edge length of\u00a0 3cm.<br \/>\nso, each unit cube has a volume of 1 cm.<br \/>\none puzzle is made up of\u00a0 3 cm<br \/>\nso, the volume of one puzzle is 27 cubic cm.<\/p>\n<p>Explanation:<br \/>\nIn the above-given figure,<br \/>\nlength = 3 cm, width = 3 cm, height = 3cm<br \/>\nvolume of the cube = l x w x h<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 3 x 3 x 3<br \/>\nvolume = 9 x 3<br \/>\nvolume = 27 cubic cm<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-15019\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-14.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 14\" width=\"194\" height=\"256\" \/><br \/>\nMultiply the volume of one puzzle by the number of puzzles<br \/>\n___ \u00d7 ___ = ____<br \/>\nSo, the volume of the box is ___.<\/p>\n<p>Answer:<br \/>\nThe volume of the box =<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 10.<br \/>\nA container holds 8 of the snowglobe boxes shown, without any gaps or overlaps. What is the volume of the container?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15020\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-15.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 15\" width=\"185\" height=\"165\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the container = 36 cubic in.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 4 x 3 x 3<br \/>\nIn the above-given figure l=4 in, w = 3 in and h = 3 in<br \/>\nvolume = 4 x 3 x 3<br \/>\nvolume = 13 x 3<br \/>\nvolume = 36 cubic in<\/p>\n<p>Question 11.<br \/>\nThe shelving unit is made of six small compartments, one medium compartment, and one large compartment. Each small compartment has a length, a width, and a height of 1 foot. What is the volume of the shelving unit?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15021\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-16.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 16\" width=\"119\" height=\"134\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the shelving unit = 4 cubic feet.<\/p>\n<p>Explanation:<br \/>\nIn the above-given question the shelving unit is made of\u00a0 six small compartments, one medium compartment, and one large compartment.<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 4 x 1 x 1<br \/>\nIn the above-given figure l=4 ft, w = 1 ft and h = 1 ft<br \/>\nvolume = 4 x 1 x 1<br \/>\nvolume = 4 x 1<br \/>\nvolume = 4 cubic feet.<\/p>\n<h3><a id=\"Understand_the_Concept_of_Volume_Homework_&amp;_Practice_13.1\"><\/a>Understand the Concept of Volume Homework &amp; Practice 13.1<\/h3>\n<p>Find the volume of the figure.<\/p>\n<p>Question 1.<br \/>\nVolume = ___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15022\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-17.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 17\" width=\"179\" height=\"71\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the figure = 15 cubic feet.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 5 x 1 x 3<br \/>\nIn the above-given figure l=5 ft, w = 1 ft and h = 3 ft<br \/>\nvolume = 5 x 1 x 3<br \/>\nvolume = 5 x 3<br \/>\nvolume = 15 cubic feet.<\/p>\n<p>Question 2.<br \/>\nVolume = ___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15023\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-18.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 18\" width=\"173\" height=\"136\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the figure = 27 cubic feet.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 3 x 3 x 3<br \/>\nIn the above-given figure l=3 ft, w = 3 ft and h = 3 ft<br \/>\nvolume = 3 x 3 x 3<br \/>\nvolume = 9 x 3<br \/>\nvolume = 27 cubic feet.<\/p>\n<p>Question 3.<br \/>\nVolume = ___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15024\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-19.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 19\" width=\"165\" height=\"109\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the figure = 10 cubic feet.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 2 x 1 x 5<br \/>\nIn the above-given figure l=2 ft, w = 1 ft and h = 5 ft<br \/>\nvolume = 2 x 1 x 5<br \/>\nvolume = 2 x 5<br \/>\nvolume = 10 cubic feet.<\/p>\n<p>Question 4.<br \/>\nVolume = ___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15025\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-20.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 20\" width=\"154\" height=\"113\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the figure = 8 cubic cm.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 2 x 2 x 2<br \/>\nIn the above-given figure l=2 cm, w = 2 cm and h = 2 cm<br \/>\nvolume = 2 x 2 x 2<br \/>\nvolume = 4 x 2<br \/>\nvolume = 8 cubic cm.<\/p>\n<p>Question 5.<br \/>\nCube-shaped boxes, like the one shown, are placed together for a display at a store. They form a solid without any gaps or overlaps that is 5 feet long, 4 feet wide, and 1 foot tall. What is the volume of the solid formed?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15026\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-21.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 21\" width=\"77\" height=\"85\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the solid formed = 20 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 5 x 4 x 1<br \/>\nIn the above-given figure l= 5 ft , w = 4 ft and h = 1 ft<br \/>\nvolume = 5 x 4 x 1<br \/>\nvolume = 20\u00a0 x 1<br \/>\nvolume = 20 cubic ft.<\/p>\n<p>Question 6.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend says the figures have the same volume. Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15027\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-22.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 22\" width=\"301\" height=\"109\" \/><\/p>\n<p>Answer:<br \/>\nYes, my friend is correct.<\/p>\n<p>Explanation:<br \/>\nIn the 1st given figure l= 4 cm, w = 1cm h = 1 cm.<br \/>\nvolume = l x w x h<br \/>\nvolume = 4 x 1 x 1<br \/>\nvolume = 4 x 1<br \/>\nvolume = 4 cubic cm<br \/>\nIn the 2nd given figure l=\u00a0 2 in , w = 1 in h = 2 in .<br \/>\nvolume = l x w x h<br \/>\nvolume = 2 x 1 x 2<br \/>\nvolume = 2 x 2<br \/>\nvolume = 4 cubic in<\/p>\n<p>Question 7.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nNewton uses 32 centimeter cubes to build a solid. The base of the solid is shown. What is the height of the solid?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15029\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-23.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 23\" width=\"148\" height=\"134\" \/><\/p>\n<p>Answer:<br \/>\nThe height of the solid = 24 cm<\/p>\n<p>Explanation:<br \/>\nIn the above-given figure, Newton uses 32-centimeter cubes to build a solid.<br \/>\nThe number of cubes filled in the solid = 8 cm cubes.<br \/>\nThe remaining cubes used to fill the solid is<br \/>\n32 &#8211; 8<br \/>\n24<br \/>\nThe height of the solid = 24 cm<\/p>\n<p>Question 8.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA container holds 27 of the spring toy boxes shown, without any gaps or overlaps. What is the volume of the container?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15028\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-23.1.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 23.1\" width=\"165\" height=\"132\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the container = 8 cubic in.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 2 x 2 x 2<br \/>\nIn the above-given figure l= 2 in , w = 2 in\u00a0 and h = 2 in.<br \/>\nvolume = 2 x 2 x 2<br \/>\nvolume = 4\u00a0 x 2<br \/>\nvolume = 8 cubic in.<\/p>\n<p>Question 9.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA store stacks boxes in an organized display. Each shaded box has a length, a width, and a height of 1 foot. What is the volume of the display?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15030\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-24.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 24\" width=\"306\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-24.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-24-300x181.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the display = 28 cubic ft.<\/p>\n<p>Explanation:<br \/>\nIn the above-given figure,<br \/>\nthe shaded box has a length, width, and height of 1 foot.<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 7 x 2 x 2<br \/>\nIn the above-given figure l= 7 ft , w = 2 ft\u00a0 and h = 2 ft.<br \/>\nvolume = 7 x 2 x 2<br \/>\nvolume = 14\u00a0 x 2<br \/>\nvolume = 28 cubic ft.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Divide.<\/p>\n<p>Question 10.<br \/>\n3 \u00f7 5 = ___<\/p>\n<p>Answer:<br \/>\nDivisor = 3<br \/>\ndividend = 5<br \/>\nQuotient = 1.6<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38556\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.3-04.png\" alt=\"\" width=\"132\" height=\"281\" \/><\/p>\n<p>Question 11.<br \/>\n1 \u00f7 4 = ___<\/p>\n<p>Answer:<br \/>\nDivisor = 1<br \/>\ndividend = 4<br \/>\nQuotient = 4<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38558\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.3-05.png\" alt=\"\" width=\"127\" height=\"294\" \/><\/p>\n<p>Question 12.<br \/>\n7 \u00f7 8 = ___<\/p>\n<p>Answer:<br \/>\nDivisor = 7<br \/>\ndividend = 8<br \/>\nQuotient = 4<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38560\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.3-06.png\" alt=\"\" width=\"126\" height=\"285\" \/><\/p>\n<h3><a id=\"Lesson_13.2_Find_Volumes_of_Right_Rectangular_Prisms\"><\/a>Lesson 13.2 Find Volumes of Right Rectangular Prisms<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>You can stack identical layers of unit cubes to build a rectangular prism.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15031\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-25.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 25\" width=\"263\" height=\"124\" \/><br \/>\nUse centimeter cubes to make one layer of a rectangular prism. Then stack identical layers and complete the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15032\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-26.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 26\" width=\"480\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-26.png 480w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-26-300x112.png 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of one layer = 9 cubic cm<br \/>\nvolume of 2 layers = 216 cubic cm<br \/>\nvolume of 3 layers = 729 cubic cm<br \/>\nvolume of 4 layers = 1,728 cubic cm<br \/>\nthe volume of prism for 1 layer = 9 cubic cm<br \/>\nthe volume of prism for 2 layers = 72 cubic cm<br \/>\nthe volume of prism for 3 layers = 729 cubic cm<br \/>\nvolume of prism for\u00a0 4 layers = 1,728 cubic cm<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nthe number of layers are 1, 2, 3, 4.<br \/>\nvolume of 1 layer = l x w x h<br \/>\nl = 3, w = 1 , h = 3<br \/>\nvolume = 3 x 1 x 3<br \/>\nv = 9 cubic cm<br \/>\nvolume of 2nd layer = l x w x h<br \/>\nl = 6, w = 6 , h = 6<br \/>\nvolume = 6 x 6 x 6<br \/>\nv = 9 cubic cm<br \/>\nvolume of 3rd layer = l x w x h<br \/>\nl = 9, w = 9 , h = 9<br \/>\nvolume = 9 x 9 x 9<br \/>\nv = 729 cubic cm<br \/>\nvolume of 4th layer = l x w x h<br \/>\nl = 12, w = 12 , h = 12<br \/>\nvolume = 12 x 12 x 12<br \/>\nv = 1,728 cubic cm<br \/>\nvolume of rectangular prism = l x w x h<br \/>\nwhere l= length, w = width and h= height<br \/>\nvolume of 1 layer = l x w x h<br \/>\nl = 3, w = 1 , h = 3<br \/>\nvolume = 3 x 1 x 3<br \/>\nv = 9 cubic cm<br \/>\nvolume of 2nd layer = l x w x h<br \/>\nl = 6, w = 6 , h = 6<br \/>\nvolume = 6 x 6 x 6<br \/>\nv = 9 cubic cm<br \/>\nvolume of 3rd layer = l x w x h<br \/>\nl = 9, w = 9 , h = 9<br \/>\nvolume = 9 x 9 x 9<br \/>\nv = 729 cubic cm<br \/>\nvolume of 4th layer = l x w x h<br \/>\nl = 12, w = 12 , h = 12<br \/>\nvolume = 12 x 12 x 12<br \/>\nvolume = 1,728 cubic cm<\/p>\n<p><strong>Precision<\/strong><br \/>\nExplain the relationship among the values in each row of the table.<\/p>\n<p><strong>Think and Grow: Find Volumes of Right Rectangular Prisms<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nA right rectangular prism is a solid figure with six rectangular faces.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15033\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-27.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 27\" width=\"177\" height=\"122\" \/><br \/>\nTo find the volume of a right rectangular prism, multiply the number of unit cubes that cover the base by the number of layers of unit cubes.<\/p>\n<p><strong>Example<\/strong><br \/>\nFind the volume of the rectangular prism.<br \/>\nEach unit cube has an edge length of ___<br \/>\nSo, each unit cube has a volume of ___.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-15034\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-28.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 28\" width=\"244\" height=\"371\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-28.png 244w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-28-197x300.png 197w\" sizes=\"(max-width: 244px) 100vw, 244px\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the rectangular prism = 24 cubic in.<br \/>\nEach unit cube has an edge length\u00a0 = 1 cm<br \/>\nso, each unit cube has a volume = 1 cubic cm<\/p>\n<p>Explanation:<br \/>\nThe volume of the rectangular prism = l x w x h<br \/>\nwhere l = length, w = width and h = height<br \/>\nIn the above figure, given that l = 4 in, w = 3 in, and h = 2 in.<br \/>\nv= 4 x 3 x 2<br \/>\nv = 12 x 2<br \/>\nv = 24 cubic in.<br \/>\neach cube has an edge length of 1 cm<br \/>\nin the above-figure shown that each cube has a length of 1 cm.<br \/>\neach cube has a volume of 1 cubic cm.<br \/>\nv = 1 x 1 x 1<br \/>\nv = 1 x 1<br \/>\nv = 1 cubic cm<\/p>\n<p>Find the number of unit cubes in a base layer. Then multiply by the number of layers to find the volume.<br \/>\nA base layer is made of ___ \u00d7 ___ = ___ unit cubes.<br \/>\nThe prism is made of _____ layers of unit cubes.<br \/>\nSo, the prism is made of ___ \u00d7 ___ = ___ unit cubes.<br \/>\nThe volume of the prism is ___.<\/p>\n<p>Answer:<br \/>\nA base layer is made up of 4 x 1 = 4 cm cubes.<br \/>\nThe prism is made up of 2 layers of unit cubes.<br \/>\nSo, the prism is made up of\u00a0 8 x 1 = 8 unit cubes.<br \/>\nThe volume of the prism = 24 cubic in<\/p>\n<p>Explanation:<br \/>\nIn the above-given figure,<br \/>\nthe base layer is made up of 4 cubes and it has 1 unit<br \/>\n4 x 1 = 4 unit cubes.<br \/>\nIn the above-given figure,<br \/>\nthe prism is made up of 2 layers of unit cubes.<br \/>\nso the prism is made up of 8 unit cubes.<br \/>\n8 x 1 = 8 unit cubes.<br \/>\nvolume of the prism = length x width x height<br \/>\nv = l x w x h<br \/>\nv = 4 x 3 x 2<br \/>\nv = 24 cubic in<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Find the volume of the rectangular prism.<\/p>\n<p>Question 1.<br \/>\nVolume = ___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-29.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 29\" width=\"235\" height=\"126\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of rectangular prism = 20 cubic\u00a0 cm.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nIn the above-given figure, l= 5 cm , w = 2 cm , h = 2 cm.<br \/>\nvolume = l x w x h<br \/>\nv = 5 x 2 x 2<br \/>\nv = 10 x 2<br \/>\nv = 20 cubic cm.<\/p>\n<p>Question 2.<br \/>\nVolume = ___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15036\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-30.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 30\" width=\"155\" height=\"159\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of rectangular prism = 18 cubic\u00a0 ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nIn the above-given figure, l= 2 ft\u00a0 , w = 3 ft\u00a0 , h = 3 ft .<br \/>\nvolume = l x w x h<br \/>\nv = 2 x 3 x 3<br \/>\nv = 6 x 3<br \/>\nv = 18 cubic ft .<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Find the volume of the rectangular prism.<\/p>\n<p>Question 3.<br \/>\nVolume = ___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15037\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-31.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 31\" width=\"151\" height=\"136\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of rectangular prism = 60 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nIn the above-given figure, l= 4 ft\u00a0 , w = 3 ft\u00a0 , h = 5 ft .<br \/>\nvolume = l x w x h<br \/>\nv = 4 x 3 x 5<br \/>\nv = 12 x 5<br \/>\nv = 60 cubic ft .<\/p>\n<p>Question 4.<br \/>\nVolume = ___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-32.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 32\" width=\"202\" height=\"94\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of rectangular prism = 36 cubic cm.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nIn the above-given figure, l= 6cm\u00a0 , w = 2 cm\u00a0 , h = 3 cm.<br \/>\nvolume = l x w x h<br \/>\nv = 6 x 2 x 3<br \/>\nv = 12 x 3<br \/>\nv = 36 cubic cm .<\/p>\n<p>Question 5.<br \/>\nVolume = ___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15039\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-33.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 33\" width=\"246\" height=\"115\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of rectangular prism = 108 cubic in.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nIn the above-given figure, l= 9 in\u00a0 , w = 3 in\u00a0 , h = 4 in.<br \/>\nvolume = l x w x h<br \/>\nv = 9 x 3 x 4<br \/>\nv = 27 x 4<br \/>\nv = 108\u00a0 cubic in .<\/p>\n<p>Question 6.<br \/>\nVolume = ___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15040\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-34.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 34\" width=\"168\" height=\"179\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of rectangular prism = 80 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nIn the above-given figure, l= 5 ft\u00a0 , w = 8 ft\u00a0 , h = 2 ft.<br \/>\nvolume = l x w x h<br \/>\nv = 5 x 8 x 2<br \/>\nv = 40 x 2<br \/>\nv = 80\u00a0 cubic ft .<\/p>\n<p>Question 7.<br \/>\nA rectangular prism is made of unit cubes, like the one shown. The prism is 6 centimeters long, 3 centimeters wide, and 4 centimeters tall. What is the volume of the prism?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15041\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-35.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 35\" width=\"49\" height=\"59\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of rectangular prism = 72 cubic cm.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nIn the above-given question, l= 6 cm\u00a0 , w = 3 cm\u00a0 , h = 4 cm.<br \/>\nvolume = l x w x h<br \/>\nv = 6 x 3 x 4<br \/>\nv = 18 x 4<br \/>\nv = 72\u00a0 cubic cm .<\/p>\n<p>Question 8.<br \/>\n<strong>Structure<\/strong><br \/>\nWhat happens to the volume of a rectangular prism when you double its height? Justify your answer by giving an example.<\/p>\n<p>Answer:<br \/>\nThe volume of the rectangular prism is increased.<\/p>\n<p>Explanation:<br \/>\nFor example, we are assuming l = 3 in , w = 2 in and h = 2 in.<br \/>\nvolume of the rectangular prism = l x w x h<br \/>\nv = 3 x 2 x 2<br \/>\nIn the above given question height is doubled.<br \/>\nh = 4<br \/>\nv = 3 x 2 x 4<br \/>\nv = 6 x 4<br \/>\nv = 24 cubic in<\/p>\n<p>Question 9.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nHow many unit cubes can fit inside the rectangular prism? Explain.<\/p>\n<p>Answer:<br \/>\n80 unit cubes can fit inside the rectangular prism.<\/p>\n<p>Explanation:<br \/>\nFor example, we are assuming l = 5 , w = 8 and h = 2 ft .<br \/>\nv = l x w x h<br \/>\nv = 5 x 8 x 2<br \/>\nv = 40\u00a0 x 2<br \/>\nv = 80 cubiic feets.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA package containing video games has a volume of 150 cubic inches. The diagram shows the number of packages that can fit in a shipping box. Estimate the volume of the shipping box.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15042\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-36.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 36\" width=\"167\" height=\"155\" \/><br \/>\nFind the number of packages in a base layer of the shipping box. Then multiply by the number of layers to find the total number of packages.<br \/>\nA base layer of the shipping box can hold 2 \u00d7 3 = 6 packages. There are 4 layers. So, the shipping box holds 4 \u00d7 6 = 24 packages.<br \/>\nMultiply the volume of 1 package by the number of packages that fit in the shipping box.<br \/>\n24 \u00d7 __ = __ cubic inches<br \/>\nSo, the volume of the shipping box is about __ cubic inches.<\/p>\n<p>Answer:<br \/>\na. The number of packages in a base layer of the shipping box = 6 packages.<br \/>\nnumber of layers = 4 and total number of packages = 6<br \/>\n6 x 4 = 24<br \/>\nThe number of packages that fit in the shipping box = 6 boxes<br \/>\n1 x\u00a0 6 = 6<br \/>\nvolume of 1 package = 1 cube.<\/p>\n<p>Explanation:<br \/>\na. The number of packages in a base layer of the shipping box = 6 packages.<br \/>\n6 x 4 = 24<br \/>\nnumber of layers = 4 and total number of packages = 6<br \/>\n6 x 4 = 24<br \/>\nThe number of packages that fit in the shipping box = 6 boxes<br \/>\n1 x\u00a0 6 = 6<br \/>\nvolume of 1 package = 1 cube.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 10.<br \/>\nA book has a volume of 91 cubic inches. The diagram shows the number of books that can fit in a container.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15043\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-37.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 37\" width=\"231\" height=\"90\" \/><br \/>\nEstimate the volume of the container.<\/p>\n<p>Answer:<br \/>\nThe volume of the container = 819 in<\/p>\n<p>Explanation:<br \/>\nIn the above-given figure,<br \/>\nA book has a volume of 91 cubic inches.<br \/>\n9 books can fit in the container .<br \/>\n91 x 9 = 819 in.<\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYour teacher stores 12 of the crates in a supply closet. The closet is 3 feet long, 2 feet wide, and 7 feet tall. How much extra space is in the closet?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15044\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-38.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 38\" width=\"206\" height=\"178\" \/><\/p>\n<p>Answer:<br \/>\nThe extra space in the closet = 43 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of closet = l x w x h<br \/>\nwhere l = length, w = width and h = height.<br \/>\nl = 3 ft , w = 2 ft and h = 7 ft.<br \/>\nv = 3 x 2 x 7<br \/>\nv = 6 x 7<br \/>\nv = 42 cubic feet<br \/>\nIn the above given figure,<br \/>\nl = 1 ft , w = 1 ft, and h = 1 ft<br \/>\nv = 1 x 1 x 1<br \/>\nv = 1 cubic cm<br \/>\nThe extra space = 42 + 1<br \/>\n43 cubic ft<\/p>\n<h3><a id=\"Find_Volumes_of_Right_Rectangular_Prisms_Homework_&amp;_Practice_13.2\"><\/a>Find Volumes of Right Rectangular Prisms Homework &amp; Practice 13.2<\/h3>\n<p>Find the volume of the rectangular prism.<\/p>\n<p>Question 1.<br \/>\nVolume = ___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15045\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-39.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 39\" width=\"198\" height=\"97\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the right rectangular prism = 30 cubic cm.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nIn the above-given figure, l= 5 cm\u00a0 , w = 2 cm\u00a0 , h = 3 cm.<br \/>\nvolume = l x w x h<br \/>\nv = 5 x 2 x 3<br \/>\nv = 10 x 3<br \/>\nv = 30\u00a0 cubic cm.<\/p>\n<p>Question 2.<br \/>\nVolume = ___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14979\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-40.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 40\" width=\"166\" height=\"117\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the right rectangular prism = 120 cubic in.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nIn the above-given figure, l= 4 in\u00a0 , w = 3 in\u00a0 , h = 3 in.<br \/>\nvolume = l x w x h<br \/>\nv = 4 x 3 x 3<br \/>\nv = 40 x 3<br \/>\nv = 120 cubic in<\/p>\n<p>Question 3.<br \/>\nVolume = ___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15046\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-41.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 41\" width=\"166\" height=\"140\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the right rectangular prism = 50 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nIn the above-given figure, l= 5 ft\u00a0 , w = 5 ft , h = 2 ft.<br \/>\nvolume = l x w x h<br \/>\nv = 5 x 5 x 2<br \/>\nv = 25 x 2<br \/>\nv = 50 cubic ft.<\/p>\n<p>Question 4.<br \/>\nVolume = ___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15047\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-42.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 42\" width=\"278\" height=\"120\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the right rectangular prism = 120 cubic cm.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nIn the above-given figure, l=10 cm\u00a0 , w = 3 cm , h = 4cm.<br \/>\nvolume = l x w x h<br \/>\nv = 10 x 3 x 4<br \/>\nv = 30 x 4<br \/>\nv = 120 cubic cm.<\/p>\n<p>Question 5.<br \/>\nA rectangular prism is made of unit cubes, like the one shown. The prism is 7 inches long, 2 inches wide, and 4 inches tall. What is the volume of the prism?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15048\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-43.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 43\" width=\"51\" height=\"60\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the right rectangular prism = 120 cubic in.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nIn the above-given question , l=7 in\u00a0 , w = 2 in , h = 4 in.<br \/>\nvolume = l x w x h<br \/>\nv = 7 x 2 x 4<br \/>\nv = 14 x 4<br \/>\nv = 176 cubic in.<\/p>\n<p>Question 6.<br \/>\n<strong>Reasoning<\/strong><br \/>\nA cube has a volume of 27 cubic inches. What is the edge length of the cube?<\/p>\n<p>Answer:<br \/>\nThe edge length of the cube = 3 in<\/p>\n<p>Explanation:<br \/>\nIn the above-given question,<br \/>\nthe volume of cube = 27 cubic inches.<br \/>\nv = l x w x h<br \/>\nv = 3 x 3 x 3<br \/>\nThe edge length of the cube = 3 in<\/p>\n<p>Question 7.<br \/>\n<strong>Reasoning<\/strong><br \/>\nYou, Newton, and Descartes each build the rectangular prism shown. You stack all three prisms on top of each other. What is the volume of the new prism? How many times greater is the volume of the new prism than the volume of your original prism?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15049\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-44.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 44\" width=\"159\" height=\"74\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the new prism = 24 cubic cm<\/p>\n<p>Explanation:<br \/>\nIn the above-given figure,<br \/>\nl = 4 cm , w = 1 cm and h = 2 cm given.<br \/>\nv = l x w x h<br \/>\nv = 4 x 1 x 2<br \/>\nv = 4 x 2<br \/>\nv = 8 cubic cm<br \/>\nI stack all 3 prisms on top of each other.<br \/>\nThe volume of the new prism = 12 x 1 x 2<br \/>\nv = 12 x 2<br \/>\nv = 24 cubic cm.<\/p>\n<p>Question 8.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA shoe box has a volume of 336 cubic inches. The diagram shows the number of shoe boxes that can fit in a shipping box. Estimate the volume of the shipping box.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15050\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-45.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 45\" width=\"307\" height=\"105\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-45.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-45-300x103.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the shipping box = 3,024 cubic in.<\/p>\n<p>Explanation:<br \/>\nGiven that a shoebox has a volume of 336 cubic inches.<br \/>\nIn the shipping box, we can fit 9 shoe boxes.<br \/>\nvolume of the shipping box = 336 x 9<br \/>\nvolume = 3,024 cubic in<\/p>\n<p>Question 9.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nThe wooden pallet can hold a maximum of 5 layers of boxes.A worker places 48 boxes, like the one shown, on to the pallet with no gaps. How many more boxes can fit?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15051\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volume-46.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 13 Understand Volume 46\" width=\"300\" height=\"160\" \/><\/p>\n<p>Answer:<br \/>\nThe more boxes can fit\u00a0 = 3 boxes.<\/p>\n<p>Explanation:<br \/>\nGiven that the wooden pallet can hold a maximum of 5 layers of boxes.<br \/>\nA worker places 48 boxes<br \/>\nThe more boxes can fit = 5 x 9<br \/>\n5 x 9 = 45 cubic ft<br \/>\n48 &#8211; 45 = 3 boxes.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Use a common denominator to write an equivalent fraction for each fraction.<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14980\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-47.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 47\" width=\"77\" height=\"54\" \/><\/p>\n<p>Answer:<br \/>\n(18\/27) , (15\/27)<\/p>\n<p>Explanation:<br \/>\nFactors of 3 = 1, 3<br \/>\nfactrs of 9 =\u00a0 1, 3 , 9<br \/>\nfrom those the common are 1, 3.<br \/>\n1 x 3 = 3<br \/>\n3 x 3 = 9<br \/>\n2 x 9 = 18<br \/>\n5 x 3 = 15<br \/>\n(18\/27) , (15\/27)<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14981\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-48.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 48\" width=\"74\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\n(7\/28) , (12\/28)<\/p>\n<p>Explanation:<br \/>\nFactors of 4 = 1, 4 and 2.<br \/>\nfactrs of 7 =\u00a0 1, 7<br \/>\nfrom those the common are 1<br \/>\n7 x 4 = 28<br \/>\n7 x 1 = 7<br \/>\n3 x 4 = 12<br \/>\n(7\/28) , (12\/28)<\/p>\n<h3><a id=\"Lesson_13.3_Apply_the_Volume_Formula\"><\/a>Lesson 13.3 Apply the Volume Formula<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Work with a partner. Use centimeter cubes to create several different rectangular prisms, each with a volume of 12 cubic centimeters. Record your results in the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14982\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-49.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 49\" width=\"126\" height=\"73\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14983\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-50.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 50\" width=\"458\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-50.png 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-50-300x157.png 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nWhat do you notice about the dimensions of each prism?<\/p>\n<p>Answer:<br \/>\nThe dimensions of each prism = 2cm, 3 cm ,2cm.<br \/>\nlength = 2 width = 3 and height = 2.<br \/>\nBase length, base width, and height<br \/>\n2, 3, 2.<br \/>\n3, 2, 2.<br \/>\n2, 2, 3.<br \/>\n4, 3, 1.<\/p>\n<p>Explanation:<br \/>\nIn the above-given question,<br \/>\nvolume of each cube = 12 cubic cm.<br \/>\nwe can assume length = 2cm width = 3cm and height = 2cm.<br \/>\notherwise we can assume length = 3 cm width = 2 cm and height = 2cm.<br \/>\nlength = 2 cm width = 2 cm and height = 3 cm.<br \/>\nlength = 4 cm width = 3 cm and height = 1 cm.<\/p>\n<p><strong>Structure<\/strong><br \/>\nHow can you find the volume of a rectangular prism without using unit cubes?<\/p>\n<p>Answer:<br \/>\nwe can find the volume of a rectangular prism by using cm cubes.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 4 in\u00a0 , w = 3 in\u00a0 , h = 3 in.<br \/>\nvolume = l x w x h<br \/>\nv = 4 x 3 x 3<br \/>\nv = 40 x 3<br \/>\nv = 120 cubic in<\/p>\n<p><strong>Think and Grow: Use a Formula to Find Volume<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nYou can use the length, width, and height of a rectangular prism to find its volume.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14984\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-51.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 51\" width=\"607\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-51.png 607w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-51-300x92.png 300w\" sizes=\"(max-width: 607px) 100vw, 607px\" \/><br \/>\nVolume of a Rectangular Prism<\/p>\n<p><strong>Example<\/strong><br \/>\nFind the volume of the rectangular prism.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14985\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-52.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 52\" width=\"667\" height=\"350\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-52.png 667w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-52-300x157.png 300w\" sizes=\"(max-width: 667px) 100vw, 667px\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of rectangular prism = 160 cubic feet.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 4 in\u00a0 , w = 3 in\u00a0 , h = 3 in.<br \/>\nvolume = l x w x h<br \/>\nv = 4 x 3 x 3<br \/>\nv = 40 x 3<br \/>\nv = 120 cubic in<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Find the volume of the rectangular prism.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14986\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-55.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 55\" width=\"172\" height=\"136\" \/><\/p>\n<p>Answer:<br \/>\nThe Volume of rectangular prism = 125 cubic cm.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 5 cm\u00a0 , w = 5 cm\u00a0 , h = 5 cm.<br \/>\nvolume = l x w x h<br \/>\nv = 5 x 5 x 5<br \/>\nv = 25 x 5<br \/>\nv = 125 cubic cm.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14987\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-56.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 56\" width=\"169\" height=\"158\" \/><\/p>\n<p>Answer:<br \/>\nThe Volume of rectangular prism = 540 cubic in.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 6 in\u00a0 , w = 9 in\u00a0 , h = 10 in.<br \/>\nvolume = l x w x h<br \/>\nv = 6 x 9 x 10<br \/>\nv = 54 x 10<br \/>\nv = 540 cubic in.<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Find the volume of the rectangular prism.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14988\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-57.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 57\" width=\"166\" height=\"146\" \/><\/p>\n<p>Answer:<br \/>\nThe Volume of rectangular prism = 60 cubic in.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 5 in\u00a0 , w = 2 in\u00a0 , h = 5 in.<br \/>\nvolume = l x w x h<br \/>\nv = 5 x 2 x 6<br \/>\nv = 10 x 6<br \/>\nv = 60 cubic in.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14989\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-58.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 58\" width=\"224\" height=\"112\" \/><\/p>\n<p>Answer:<br \/>\nThe Volume of rectangular prism = 108 cubic cm.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 9 cm\u00a0 , w = 4 cm\u00a0 , h = 3 cm .<br \/>\nvolume = l x w x h<br \/>\nv = 9 x 4 x 3<br \/>\nv = 36 x 3<br \/>\nv = 108 cubic cm.<\/p>\n<p>Question 5.<br \/>\nNewton\u2019s dog house is a rectangular prism. The house is 5 feet long, 4 feet wide, and 5 feet tall. What is the volume of the house?<\/p>\n<p>Answer:<br \/>\nThe Volume of house = 100 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 5 ft\u00a0 , w = 4 ft\u00a0 , h = 5 ft .<br \/>\nvolume = l x w x h<br \/>\nv = 5 x 4 x 5<br \/>\nv = 20 x 5<br \/>\nv = 100 cubic ft.<\/p>\n<p>Question 6.<br \/>\nA hole dug for an in-ground swimming pool is a rectangular prism. The hole is 20 feet long, 10 feet wide, and 6 feet tall. What is the volume of the hole?<\/p>\n<p>Answer:<br \/>\nThe Volume of the hole = 1200 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 20 ft\u00a0 , w = 10 ft\u00a0 , h = 6 ft .<br \/>\nvolume = l x w x h<br \/>\nv = 20 x 10 x 6<br \/>\nv = 200 x 6<br \/>\nv = 1200 cubic ft.<\/p>\n<p>Question 7.<br \/>\n<strong>Structure<\/strong><br \/>\nCompare the dimensions and volumes of the three rectangular prisms. What do you notice?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-59.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 59\" width=\"608\" height=\"140\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-59.png 608w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-59-300x69.png 300w\" sizes=\"(max-width: 608px) 100vw, 608px\" \/><\/p>\n<p>Answer:<br \/>\nThe dimensions and volumes of the 3 rectangular prisms are equal volumes.<\/p>\n<p>Explanation:<br \/>\nvolume of the 1st rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 4 in\u00a0 , w = 6 in\u00a0 , h = 3 in .<br \/>\nvolume = l x w x h<br \/>\nv = 4 x 6 x 3<br \/>\nv = 24 x 3<br \/>\nv = 72 cubic in.<br \/>\nvolume of the 3rd rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 6 in\u00a0 , w = 3 in\u00a0 , h = 4 in .<br \/>\nvolume = l x w x h<br \/>\nv = 6 x 3 x 4<br \/>\nv = 18 x 4<br \/>\nv = 72 cubic in.<br \/>\nvolume of the 2nd rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 3 in\u00a0 , w = 4 in\u00a0 , h = 6 in .<br \/>\nvolume = l x w x h<br \/>\nv = 3 x 4 x 6<br \/>\nv = 12 x 6<br \/>\nv = 72 cubic in.<\/p>\n<p>Question 8.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWhat is the volume of Newton\u2019s rectangular prism?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14991\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-60.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 60\" width=\"215\" height=\"188\" \/><\/p>\n<p>Answer:<br \/>\nvolume of the Newtons rectangular prism = 400 cubic cm<\/p>\n<p>Explanation:<br \/>\nvolume of the Newtons rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l= 2 cm , w = 6 in\u00a0 , h = 3 in .<br \/>\nheight = 5times of length = 5 x 2 = 10 cm<br \/>\nwidth = 2 times of height = 10 x 2 = 20 cm<br \/>\nvolume = l x w x h<br \/>\nv = 2 x 20 x 10<br \/>\nv = 40 x 10<br \/>\nv = 400 cubic cm.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nThe dump truck bed is a rectangular prism. The area of the base is 8 square yards.The height is 2 yards. The driver needs to transport 18 cubic yards of gravel. Can he transport all of the gravel at once?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14992\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-61.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 61\" width=\"207\" height=\"149\" \/><br \/>\nUse a formula to find the volume of the dump truck bed.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14993\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-62.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 62\" width=\"429\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-62.png 429w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-62-300x76.png 300w\" sizes=\"(max-width: 429px) 100vw, 429px\" \/><br \/>\nThe volume of the dump truck bed is ___.<br \/>\nCompare the volume of the bed to the amount of gravel.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14994\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-63.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 63\" width=\"111\" height=\"49\" \/><br \/>\nSo, the driver __ transport all of the gravel at once.<\/p>\n<p>Answer:<br \/>\nThe volume of dump truck bed = 16 sq yards.<br \/>\nthe volume of bed to the amount of gravel = 16: 18<br \/>\nso, the driver cannot transport all of the gravel at once.<\/p>\n<p>Explanation:<br \/>\nThe volume of dump truck bed\u00a0 = base x height<br \/>\nv = b x h<br \/>\nwhere base = 8 yds and height = 2 yards.<br \/>\nv = 8 x 2<br \/>\nv = 16 sq yds.<br \/>\nvolume of bed to the amount of gravel is 18 yards given.<br \/>\n16: 18<br \/>\nso, the driver cannot transport all of the gravel at once.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 9.<br \/>\nThe aquarium is a rectangular prism. The area of the base is 288 square inches. Can the aquarium hold 4,500 cubic inches of water? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14995\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-64.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 64\" width=\"215\" height=\"133\" \/><\/p>\n<p>Answer:<br \/>\nYes, the aquarium can hold 4,500 cubic inches of water.<\/p>\n<p>Explanation:<br \/>\nthe volume of rectangular prism = base x height<br \/>\narea = 288 sq inches given . height = 16 in<br \/>\nvolume = 288 x 16<br \/>\nv = 4608 cubic in.<br \/>\nThe aquarium can hold 4,500 cubic in of water.<\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA principal orders two types of lockers for the school. Which locker has a greater volume? How much greater?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14996\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-65.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 65\" width=\"258\" height=\"245\" \/><\/p>\n<p>Answer:<br \/>\nLocker B has greater volume than Locker A.<\/p>\n<p>Explanation:<br \/>\nvolume of the Locker A = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 12 in\u00a0 , w = 15 in\u00a0 , h = 6 in .<br \/>\nvolume = l x w x h<br \/>\nv = 12 x 15 x 6<br \/>\nv = 180 x 6<br \/>\nv = 1080 cubic in.<br \/>\nvolume of the Locker B = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 15 in\u00a0 , w = 15 in\u00a0 , h = 5 in .<br \/>\nvolume = l x w x h<br \/>\nv = 15 x 15 x 5<br \/>\nv = 225 x 5<br \/>\nv = 1125 cubic in.<\/p>\n<h3><a id=\"Apply_the_Volume_Formula_Homework_&amp;_Practice_13.3\"><\/a>Apply the Volume Formula Homework &amp; Practice 13.3<\/h3>\n<p>Find the volume of the rectangular prism.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14997\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-66.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 66\" width=\"176\" height=\"149\" \/><\/p>\n<p>Answer:<br \/>\nThe Volume of the rectangular prism = 64 cubic in.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 4 in , w = 4 in , h = 4 in .<br \/>\nvolume = l x w x h<br \/>\nv = 4 x 4 x 4<br \/>\nv = 16 x 4<br \/>\nv = 64 cubic in.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14998\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-67.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 67\" width=\"212\" height=\"112\" \/><\/p>\n<p>Answer:<br \/>\nThe Volume of the rectangular prism = 120 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 8 ft , w = 5 ft , h = 3 ft .<br \/>\nvolume = l x w x h<br \/>\nv = 8 x 5 x 3<br \/>\nv = 40 x 3<br \/>\nv = 120 cubic ft.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-68.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 68\" width=\"131\" height=\"139\" \/><\/p>\n<p>Answer:<br \/>\nThe Volume of the rectangular prism = 56 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 4 ft , w = 2ft , h = 7 ft .<br \/>\nvolume = l x w x h<br \/>\nv = 4 x 2 x 7<br \/>\nv = 8 x 7<br \/>\nv = 56 cubic ft.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-69.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 69\" width=\"195\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\nThe Volume of the rectangular prism = 120 cubic cm.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 6 cm , w = 5 cm , h = 4 cm .<br \/>\nvolume = l x w x h<br \/>\nv = 6 x 5 x 4<br \/>\nv = 30 x 4<br \/>\nv = 120 cubic cm.<\/p>\n<p>Question 5.<br \/>\nA toy chest is a rectangular prism. The chest is 4 feet long, 2 feet wide, and 2 feet tall. What is the volume of the chest?<\/p>\n<p>Answer:<br \/>\nThe Volume of the chest = 16 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 4 ft , w = 2 ft , h = 2 ft .<br \/>\nvolume = l x w x h<br \/>\nv = 4 x 2 x 2<br \/>\nv = 8 x 2<br \/>\nv = 16 cubic ft.<\/p>\n<p>Question 6.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend uses the formula V = B \u00d7 h and finds V = 10 \u00d7 9 = 90 cubic inches. Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15001\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-70.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 70\" width=\"202\" height=\"112\" \/><\/p>\n<p>Answer:<br \/>\nNo, my friend is not correct.<\/p>\n<p>Explanation:<br \/>\nvolume = base x height<br \/>\nv = 9 x 5<br \/>\nwhere base = 9 in, height = 5 in given.<br \/>\nv = 45 cubic in.<\/p>\n<p>Question 7.<br \/>\n<strong>Number Sense<\/strong><br \/>\nFind the volume of the rectangular prism. Then double the dimensions of the prism and \ufb01nd the new volume. How does the new volume compare to the original volume?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15002\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-71.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 71\" width=\"164\" height=\"147\" \/><\/p>\n<p>Answer:<br \/>\nThe new Volume of the prism= 3600 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 4 in , w = 3 in , h = 5 in .<br \/>\nvolume = l x w x h<br \/>\nv = 4 x 3 x 5<br \/>\nv = 12\u00a0 x 5<br \/>\nv =\u00a0 60 cubic in.<br \/>\nGiven that the dimensions are doubled.<br \/>\n4 x 4 = 16 , 3 x 3 = 9, 5 x 5 = 25<br \/>\nvolume of the new rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 16 in , w = 9 in , h = 25 in .<br \/>\nvolume = l x w x h<br \/>\nv = 16 x 9 x 25<br \/>\nv = 144\u00a0 x 25<br \/>\nv =\u00a0 3600 cubic in.<\/p>\n<p>Question 8.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA sandbox is a rectangular prism. The area of the base is 3,600 square inches. The height is 11 inches. You add 38,000 cubic inches of sand to the box. Do you \ufb01ll the sandbox to the top? Explain.<\/p>\n<p>Answer:<br \/>\nYes, we can fill the sandbox to the top.<\/p>\n<p>Explanation:<br \/>\nvolume = base x height<br \/>\nv = 3600 x 11<br \/>\nv = 39,600 cubic in.<br \/>\nif\u00a0 we add 38,000 cubic inches of sand to the box<br \/>\n39,600 + 38,000<br \/>\n77,600\u00a0 inches.<\/p>\n<p>Question 9.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nEach piece of Descartes\u2019s clubhouse is a cube. What is the volume of the clubhouse? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15003\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-72.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 72\" width=\"157\" height=\"192\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the clubhouse = 6 cubic feet.<\/p>\n<p>Explanation:<br \/>\nvolume of the cube = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l= 3 ft , w = 2 ft , h = 1 ft .<br \/>\nvolume = l x w x h<br \/>\nv = 3 x 2 x 1<br \/>\nv = 6\u00a0 x 1<br \/>\nv =\u00a0 6 cubic ft.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Find the quotient. Then check your answer.<\/p>\n<p>Question 10.<br \/>\n3.38 \u00f7 2.6 = ___<\/p>\n<p>Answer:<br \/>\nQuotient = 1.3<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38551\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.3-01.png\" alt=\"\" width=\"182\" height=\"344\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.3-01.png 182w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.3-01-159x300.png 159w\" sizes=\"(max-width: 182px) 100vw, 182px\" \/><\/p>\n<p>Question 11.<br \/>\n6.12 \u00f7 1.53 = __<\/p>\n<p>Answer:<br \/>\nQuotient = 4.0<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38552\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.3-02.png\" alt=\"\" width=\"216\" height=\"394\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.3-02.png 216w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.3-02-164x300.png 164w\" sizes=\"(max-width: 216px) 100vw, 216px\" \/><\/p>\n<p>Question 12.<br \/>\n0.63 \u00f7 0.9 = ___<\/p>\n<p>Answer:<br \/>\nQuotient = 0.7<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38553\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.3-03.png\" alt=\"\" width=\"134\" height=\"284\" \/><\/p>\n<h3><a id=\"Lesson_13.4_Find_Unknown_Dimensions\"><\/a>Lesson 13.4 Find Unknown Dimensions<\/h3>\n<p>Explore and Grow<\/p>\n<p>For each row of the table, use centimeter cubes to create the rectangular prism described. Then complete the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-73.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 73\" width=\"121\" height=\"85\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15005\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-74.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 74\" width=\"533\" height=\"189\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-74.png 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-74-300x106.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p><strong>Construct Arguments<\/strong><br \/>\nExplain how you determined the unknown dimension for each rectangular prism.<\/p>\n<p>Answer:<br \/>\nvolume = 8, length = 2cm, width = 2 cm, height = 2 cm.<br \/>\nvolume = 15, length = 5cm, width = 3 cm, height = 1 cm.<br \/>\nvolume = 24, length = 8cm, width = 2 cm, height = 4 cm.<br \/>\nvolume = 36, length = 4cm, width = 3 cm, height = 3 cm.<\/p>\n<p>Explanation:<br \/>\nVolume of rectangular prism = l x w x h<br \/>\nlength = 2cm, width = 2cm given.<br \/>\nvolume = 2 x 2 x 2<br \/>\nv = 8 cubic cm, h = 2 cm<br \/>\nVolume of rectangular prism = l x w x h<br \/>\nlength = 5cm, height= 1cm given.<br \/>\nvolume = 2 x 3 x 1<br \/>\nv = 15 cubic cm, w = 3 cm<br \/>\nVolume of rectangular prism = l x w x h<br \/>\nwidth = 2cm, height= 4cm given.<br \/>\nvolume =3\u00a0 x 2 x 4<br \/>\nv = 24 cubic cm, l = 3 cm<br \/>\nVolume of rectangular prism = l x w x h<br \/>\nlength = 4cm, width= 3cm given.<br \/>\nvolume =4 x 3 x 3<br \/>\nv = 36 cubic cm, h = 3 cm<\/p>\n<p><strong>Think and Grow: Find Unknown Dimensions<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nThe volume of the rectangular prism is 56 cubic feet. Find the height.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15006\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-75.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 75\" width=\"606\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-75.png 606w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-75-300x119.png 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<p>Answer:<br \/>\nThe height of the rectangular prism = cm<\/p>\n<p>Explanation:<br \/>\nGiven that volume of rectangular prism = 56 cubic feet.<br \/>\nvolume = base x height<br \/>\nv = 56 given base = 8<br \/>\n56 = 8 x h<br \/>\nh = (56\/8)<br \/>\nh = 7 cm<\/p>\n<p><strong>Example<\/strong><br \/>\nThe volume of the rectangular prism is 180 cubic centimeters. Find the length.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15007\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-76.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 76\" width=\"619\" height=\"312\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-76.png 619w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-76-300x151.png 300w\" sizes=\"(max-width: 619px) 100vw, 619px\" \/><\/p>\n<p>Answer:<br \/>\nThe length of prism = 9 cm<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven , w = 5 cm , h = 4 cm .<br \/>\nvolume = l x w x h<br \/>\n180 = l x 5 x 4<br \/>\n180 = l x 20<br \/>\n180 = 20 l<br \/>\nl = (180\/20)<br \/>\nl = 9 cm.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Find the unknown dimension of the rectangular prism.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15008\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-77.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 77\" width=\"196\" height=\"102\" \/><\/p>\n<p>Answer:<br \/>\nThe height of prism = 1 cm<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven , l = 3 cm , w = 4 cm .<br \/>\nvolume = l x w x h<br \/>\n12 = 3 x 4 x h<br \/>\n12 = l2 x h<br \/>\n12 = 12h<br \/>\nh= (20\/20)<br \/>\nh = 1 cm.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15009\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-78.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 78\" width=\"109\" height=\"146\" \/><\/p>\n<p>Answer:<br \/>\nThe width of prism = 1 cm<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven , l = 3 cm , h = 9 cm .<br \/>\nvolume = l x w x h<br \/>\n27 = 3 x w x 9<br \/>\n27 = 27 w<br \/>\nw= (27\/27)<br \/>\nw = 1 cm.<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Find the unknown dimension of the rectangular prism.<\/p>\n<p>Question 3.<br \/>\nVolume = 400 cubic inches<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15010\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-79.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 79\" width=\"196\" height=\"141\" \/><\/p>\n<p>Answer:<br \/>\nThe height of the rectangular prism = 8 in<\/p>\n<p>Explanation:<br \/>\nGiven that volume of rectangular prism = 56 cubic feet.<br \/>\nvolume = base x height<br \/>\nv = 400 given base = 50<br \/>\n400 = 50 x h<br \/>\nh = (400\/50)<br \/>\nh = 8 in<\/p>\n<p>Question 4.<br \/>\nVolume = 343 cubic centimeters<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15011\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-80.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 80\" width=\"163\" height=\"124\" \/><\/p>\n<p>Answer:<br \/>\nThe length of the rectangular prism = 8 in<\/p>\n<p>Explanation:<br \/>\nGiven that volume of rectangular prism = 56 cubic feet.<br \/>\nvolume = base x height<br \/>\nv = 343 given base = 49 sq cm<br \/>\n343 = 49 x l<br \/>\nl = (343\/49)<br \/>\nl = 8 in<\/p>\n<p>Question 5.<br \/>\nVolume = 132 cubic feet<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-15012\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume-81.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume 81\" width=\"190\" height=\"166\" \/><\/p>\n<p>Answer:<br \/>\nThe height of the rectangular prism = 11 ft<\/p>\n<p>Explanation:<br \/>\nGiven that volume of rectangular prism = 132cubic feet.<br \/>\nvolume = base x height<br \/>\nv = 132 given base = 12 sq ft<br \/>\n132 = 12 x h<br \/>\nh = (132\/12)<br \/>\nh = 11 ft<\/p>\n<p>Question 6.<br \/>\nVolume = 512 cubic inches<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14912\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-82.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 82\" width=\"278\" height=\"122\" \/><\/p>\n<p>Answer:<br \/>\nThe Width of the rectangular prism = 8 in.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l=16 in , v = 512 cubicin , h = 4 in.<br \/>\nvolume = l x w x h<br \/>\n512 = 16 x w x 4<br \/>\n512 = w x 64<br \/>\n512 = 64 w<br \/>\nw = (512\/64)<br \/>\nw = 8 in<\/p>\n<p>Question 7.<br \/>\n<strong>Writing<\/strong><br \/>\nExplain how to find an unknown dimension of a rectangular prism given its volume and the other two dimensions.<\/p>\n<p>Answer:<br \/>\nThe Width of the rectangular prism = 8 in.<\/p>\n<p>Explanation:<br \/>\nWe have to assume v = 512 cubic in, l= 16 and h= 4 in<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\nAssume, l=16 in , v = 512 cubicin , h = 4 in.<br \/>\nvolume = l x w x h<br \/>\n512 = 16 x w x 4<br \/>\n512 = w x 64<br \/>\n512 = 64 w<br \/>\nw = (512\/64)<br \/>\nw = 8 in<\/p>\n<p>Question 8.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA rectangular prism has a volume of 720 cubic centimeters. The height of the prism is 10 centimeters. The length is twice the width. What are the dimensions of the base?<\/p>\n<p>Answer:<br \/>\nThe dimensions of the base = 72 cm<\/p>\n<p>Explanation:<br \/>\nGiven that volume of rectangular prism = 720 cubic cm.<br \/>\nvolume = base x height<br \/>\nv = 720 given h = 10<br \/>\n720 = b x 10<br \/>\n720 =10 b<br \/>\nb = (720\/10)<br \/>\nb = 72 cm<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA traveler buys the painting shown. The volume of the suitcase is 1,820 cubic inches. Can the painting lie \ufb02at inside the suitcase?<br \/>\nUse a formula to \ufb01nd the length of the suitcase.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-83.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 83\" width=\"631\" height=\"338\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-83.png 631w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-83-300x161.png 300w\" sizes=\"(max-width: 631px) 100vw, 631px\" \/><\/p>\n<p>Answer:<br \/>\nYes, the painting lies flat inside the suitcase.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height.<br \/>\ngiven , v = 1,820 , \u00a0h = 7 in, w = 13 in .<br \/>\nvolume = l x w x h<br \/>\n1820 = l x 13x 7<br \/>\n1820 = l x 91<br \/>\nl = (1820\/91)<br \/>\nl = 20 in<br \/>\nThe area of the painting = l x w<br \/>\npainting is in the shape of a rectangle<br \/>\narea of rectangle = l x w<br \/>\narea = 14 x 11<br \/>\narea = 154<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 9.<br \/>\nThe volume of the candle is 576 cubic centimeters. Will the candle fit completely inside the glass jar? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14914\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-85.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 85\" width=\"293\" height=\"177\" \/><\/p>\n<p>Answer:<br \/>\nYes, the candle will fit completely inside the glass jar.<\/p>\n<p>Explanation:<br \/>\nGiven that volume of candle = 576 cubic cm.<br \/>\nvolume = base x height<br \/>\nv = 576 given b = 36 sq cm<br \/>\n576 = 36 x h<br \/>\n576= 36 h<br \/>\nh = (576\/36)<br \/>\nh = 16 cm<br \/>\nGiven that volume of glass jar = 576 cubic cm.<br \/>\nvolume = base x height<br \/>\ngiven b = 64 sq cm h = 12 cm<br \/>\nv = 64 x 12<br \/>\nv= 768 cubic cm<\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe popcorn boxes have the same volume, but different dimensions. What is the width of Box B?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14915\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-86.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 86\" width=\"260\" height=\"190\" \/><\/p>\n<p>Answer:<br \/>\nThe Width of the Box B\u00a0 = 3 in.<\/p>\n<p>Explanation:<br \/>\nvolume of the Box A = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=5 in , w = 2 in , h = 9 in.<br \/>\nvolume = l x w x h<br \/>\nv = 5 x 2 x 9<br \/>\nv = 10 x 9<br \/>\nv = 90 cubic in<br \/>\nvolume of the Box B = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=5 in , v = 90 cubic in , h = 6 in.<br \/>\nvolume = l x w x h<br \/>\n90 = 5 x w x 6<br \/>\n90 = 30 x w<br \/>\n90 = 30 w<br \/>\nw = (90\/30)<br \/>\nw = 3 in<\/p>\n<h3><a id=\"Find_Unknown_Dimensions_Homework_&amp;_Practice_13.4\"><\/a>Find Unknown Dimensions Homework &amp; Practice 13.4<\/h3>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14916\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-87.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 87\" width=\"200\" height=\"127\" \/><\/p>\n<p>Answer:<br \/>\nThe unknown dimensions are l= 6in, w= 2 in,and h = 1 in.<\/p>\n<p>Explanation:<br \/>\ngiven that area of the base = 12 sq in<br \/>\narea = l x w<br \/>\n12 = 6 x 2<br \/>\nv = l x w x h<br \/>\n12 = 6 x 2h<br \/>\n12 = 12 h<br \/>\nh = (12\/12)<br \/>\nh = 1 in<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14917\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-88.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 88\" width=\"180\" height=\"121\" \/><\/p>\n<p>Answer:<br \/>\nlength of the prism = 1 cm<\/p>\n<p>Explanation:<br \/>\nGiven that volume of prism = 30 cubic cm.<br \/>\nvolume = length x base x height<br \/>\ngiven b = 6 cm h = 5 cm<br \/>\n30 =\u00a0 l x 6 x 5<br \/>\n30= 30 l<br \/>\nl = (30\/30)<br \/>\nl = 1 cm<\/p>\n<p>Find the unknown dimension of the rectangular prism.<\/p>\n<p>Question 3.<br \/>\nVolume = 480 cubic feet<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14918\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-89.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 89\" width=\"262\" height=\"97\" \/><\/p>\n<p>Answer:<br \/>\nThe height of the rectangular prism = 2 ft<\/p>\n<p>Explanation:<br \/>\nGiven that volume of rectangular prism = 56 cubic feet.<br \/>\nvolume = base x height<br \/>\nv = 480 cubic feet given base = 240 sq ft<br \/>\n480 = 240 x h<br \/>\n480 = 240 h<br \/>\nh = (480\/240)<br \/>\nh = (48\/24)<br \/>\nh = 2 ft<\/p>\n<p>Question 4.<br \/>\nVolume = 351 cubic inches<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14919\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-90.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 90\" width=\"129\" height=\"163\" \/><\/p>\n<p>Answer:<br \/>\nThe Width of the prism =7.3125 in<\/p>\n<p>Explanation:<br \/>\nvolume of the Box B = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=3 in , v = 351 cubic in ,\u00a0 h = 13 in.<br \/>\nvolume = l x w x h<br \/>\n351 = 3 x w x 16<br \/>\n351 = 48 x w<br \/>\n351 = 48 w<br \/>\nw = (351\/48)<br \/>\nw = 7.3125 in<\/p>\n<p>Question 5.<br \/>\n<strong>Open-Ended<\/strong><br \/>\nA rectangular prism has a volume of 144 cubic feet. The height of the prism is 6 feet. Give one possible pair of dimensions for the base.<\/p>\n<p>Answer:<br \/>\nThe base of the rectangular prism = 24 ft<\/p>\n<p>Explanation:<br \/>\nGiven that volume of rectangular prism = 144 cubic feet.<br \/>\nvolume = base x height<br \/>\nv = 144 cubic feet given height = 6 ft<br \/>\n144 = b x 6<br \/>\n144 = 6b<br \/>\nb = (144\/6)<br \/>\nb = 24 feet<\/p>\n<p>Question 6.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe volume of the rectangular prism is 64 cubic centimeters. What is the value of y?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14920\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-91.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 91\" width=\"118\" height=\"104\" \/><\/p>\n<p>Answer:<br \/>\nThe value of y = 4 cm<\/p>\n<p>Explanation:<br \/>\nGiven that the volume of rectangular prism = 64 cubic in.<br \/>\nv = l x w x h<br \/>\n64 = lwh<br \/>\n64 = 4 x 4 x 4<br \/>\n64 = 16\u00a0 x 4<br \/>\n64 = 64<\/p>\n<p>Question 7.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nThe volume of the gift is 900 cubic inches. Can the gift fit inside the shipping box? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14921\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-92.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 92\" width=\"293\" height=\"157\" \/><\/p>\n<p>Answer:<br \/>\nYes, the gift will fit\u00a0 inside the shipping box.<\/p>\n<p>Explanation:<br \/>\nGiven that volume of gift = 900 cubic in.<br \/>\nvolume = base x height<br \/>\nv = 900 given b = 100 sq in<br \/>\n900 = 100 x h<br \/>\n900= 100h<br \/>\nh = (900\/100)<br \/>\nh = 9 in<br \/>\nGiven that base of shipping box = 576 cubic cm.<br \/>\nvolume = base x height<br \/>\ngiven b = 144 sq in h = 10 in<br \/>\nv = 144 x 10<br \/>\nv= 1440 cubic in.<\/p>\n<p>Question 8.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou fill the entire fish tank with water. Then you dump out some of the water.The volume of the water in the tank decreases by 96 cubic inches. How deep is the water now?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14922\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-93.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 93\" width=\"171\" height=\"161\" \/><\/p>\n<p>Answer:<br \/>\nThe water in the tank\u00a0 = 480 cubic in.<\/p>\n<p>Explanation:<br \/>\nvolume of the Box A = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=8 in , w = 6 in , h = 12 in.<br \/>\nvolume = l x w x h<br \/>\nv = 8 x 6 x 12<br \/>\nv = 48 x 12<br \/>\nv = 576 cubic in<br \/>\ngiven that volume of water in the tank is decreased by 96 cubic in.<br \/>\nv = 576 &#8211; 96<br \/>\nv = 480 cubic in.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Divide.<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14923\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-94.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 94\" width=\"119\" height=\"54\" \/><\/p>\n<p>Answer:<br \/>\nDivisor = 0.3<br \/>\nDividend = 2<br \/>\nRemainder = 2<br \/>\nQuotient = 6.6<\/p>\n<p>Explanation:<br \/>\n(1\/3) = 0.33<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38621\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.4-02.png\" alt=\"\" width=\"154\" height=\"353\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.4-02.png 154w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.4-02-131x300.png 131w\" sizes=\"(max-width: 154px) 100vw, 154px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14924\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-95.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 95\" width=\"128\" height=\"59\" \/><\/p>\n<p>Answer:<br \/>\nDivisor = 0.1<br \/>\nDividend = 6<br \/>\nRemainder = 0<br \/>\nQuotient = 60<\/p>\n<p>Explanation:<br \/>\n(1\/10) = 0.1<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38622\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.4-03.png\" alt=\"\" width=\"155\" height=\"348\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.4-03.png 155w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.4-03-134x300.png 134w\" sizes=\"(max-width: 155px) 100vw, 155px\" \/><\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14925\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-96.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 96\" width=\"123\" height=\"60\" \/><\/p>\n<p>Answer:<br \/>\nDivisor = 0.125<br \/>\nDividend = 4<br \/>\nRemainder = 0<br \/>\nQuotient = 32<\/p>\n<p>Explanation:<br \/>\n(1\/10) = 0.125<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38623\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.4-04.png\" alt=\"\" width=\"230\" height=\"451\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.4-04.png 230w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.4-04-153x300.png 153w\" sizes=\"(max-width: 230px) 100vw, 230px\" \/><\/p>\n<h3><a id=\"Lesson_13.5_Find_Volumes_of_Composite_Figures\"><\/a>Lesson 13.5 Find Volumes of Composite Figures<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Use centimeter cubes to find the volume of the figure. Explain your method.<br \/>\nAnswer:<br \/>\nvolume of figure 1 = 60 cubic cm.<br \/>\nvolume of figure 2 = 36 cubic cm.<\/p>\n<p>Explanation:<br \/>\nvolume of the figure 1( left side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=6 cm , w = 2 cm , h = 5 cm.<br \/>\nvolume = l x w x h<br \/>\nv = 6 x 2 x 5<br \/>\nv = 12 x 5<br \/>\nv = 60 cubic cm<br \/>\nvolume of the figure 2 (right side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=6 cm , v = 3 cm , h = 2 cm.<br \/>\nvolume = l x w x h<br \/>\nv = 6 x 3 x 2<br \/>\nv = 18 x 2<br \/>\nv = 36 cubic cm.<\/p>\n<p><strong>Structure<\/strong><br \/>\nDescribe another way to find the volume of the figure<\/p>\n<p><strong>Think and Grow: Find the Volume of a Composite Figure<\/strong><\/p>\n<p><strong>Key Idea<\/strong><\/p>\n<p>A composite figure is made of two or more composite figure solid figures. You can break apart a composite figure to find its volume.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14927\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-98.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 98\" width=\"175\" height=\"133\" \/><\/p>\n<p><strong>Example<\/strong><br \/>\nFind the volume of the composite figure.<\/p>\n<p>Break apart the figure into rectangular prisms. Find the dimensions of each prism.<\/p>\n<p>Answer:<br \/>\nvolume of figure 1 = 320 cubic ft.<br \/>\nvolume of figure 2 = 1200 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the figure 2( right side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=10 ft , w = 4 ft , h = 3 ft.<br \/>\nvolume = l x w x h<br \/>\nv = 10 x 4 x 3<br \/>\nv = 40 x 3<br \/>\nv = 1200 cubic ft.<br \/>\nvolume of the figure 1 (left side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=10 ft , w = 4 ft , h = 8 ft.<br \/>\nvolume = l x w x h<br \/>\nv = 10 x 4 x 8<br \/>\nv = 40 x 8<br \/>\nv = 320 cubic feet.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 1.<br \/>\nFind the volume of the composite figure.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14929\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-102.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 102\" width=\"208\" height=\"140\" \/><\/p>\n<p>Answer:<br \/>\nvolume of figure 1 = 60 cubic cm.<br \/>\nvolume of figure 2 = 990 cubic cm.<\/p>\n<p>Explanation:<br \/>\nvolume of the figure 1( left side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=10 cm , w = 2 cm , h = 3 cm.<br \/>\nvolume = l x w x h<br \/>\nv = 10 x 2 x 3<br \/>\nv = 20 x 3<br \/>\nv = 60 cubic cm.<br \/>\nvolume of the figure 2 (right side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=10 cm , w = 11 cm , h = 9 cm.<br \/>\nvolume = l x w x h<br \/>\nv = 10 x 11 x 9<br \/>\nv = 110 x 9<br \/>\nv = 990 cubic cm<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Find the volume of the composite figure.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14930\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-103.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 103\" width=\"232\" height=\"180\" \/><\/p>\n<p>Answer:<br \/>\nvolume of figure 1 = 360 cubic in.<br \/>\nvolume of figure 2 = 360 cubic in.<\/p>\n<p>Explanation:<br \/>\nvolume of the figure 1( left side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=12 in , w = 3 in , h = 10 in.<br \/>\nvolume = l x w x h<br \/>\nv = 12 x 3 x 10<br \/>\nv = 36 x 10<br \/>\nv = 360 cubic in.<br \/>\nvolume of the figure 2 (right side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=12 in , w = 5 in , h = 6 in.<br \/>\nvolume = l x w x h<br \/>\nv = 12 x 5 x 6<br \/>\nv = 60 x 6<br \/>\nv = 360 cubic in .<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14931\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-104.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 104\" width=\"229\" height=\"167\" \/><\/p>\n<p>Answer:<br \/>\nvolume of figure 1 = 720 cubic ft.<br \/>\nvolume of figure 2 = 120 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the figure 1( left side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=15 ft , w = 6 ft , h = 8 ft.<br \/>\nvolume = l x w x h<br \/>\nv = 15 x 6 x 8<br \/>\nv = 90 x 8<br \/>\nv = 720 cubic ft.<br \/>\nvolume of the figure 2 (right side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=10 ft , w = 4 ft , h = 3 ft.<br \/>\nvolume = l x w x h<br \/>\nv = 10 x 4 x 3<br \/>\nv = 40 x 3<br \/>\nv = 120 cubic ft<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14932\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-105.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 105\" width=\"312\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-105.png 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-105-300x108.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/p>\n<p>Answer:<br \/>\nvolume of figure 1 = 720 cubic ft.<br \/>\nvolume of figure 2 = 120 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the figure 1( left side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=20 cm , w = 5 cm , h = 1 cm.<br \/>\nvolume = l x w x h<br \/>\nv = 20 x 5 x 1<br \/>\nv = 100 x 8<br \/>\nv = 720 cubic ft.<br \/>\nvolume of the figure 2 (right side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=10 ft , w = 4 ft , h = 3 ft.<br \/>\nvolume = l x w x h<br \/>\nv = 10 x 4 x 3<br \/>\nv = 40 x 3<br \/>\nv = 120 cubic ft<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14933\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-106.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 106\" width=\"262\" height=\"153\" \/><\/p>\n<p>Answer:<br \/>\nvolume of figure 1 = 132 cubic ft.<br \/>\nvolume of figure 2 = 52 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the figure 2( right side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=9 ft , w = 3 ft , h = 2 ft.<br \/>\nvolume = l x w x h<br \/>\nv = 9 x 3 x 2<br \/>\nv = 27 x 2<br \/>\nv = 52 cubic ft.<br \/>\nvolume of the figure 1 (left side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=11ft , w = 6 ft , h = 2 ft.<br \/>\nvolume = l x w x h<br \/>\nv = 11 x 6 x 2<br \/>\nv = 66 x 2<br \/>\nv = 132 cubic ft.<\/p>\n<p>Question 6.<br \/>\n<strong>Number Sense<\/strong><br \/>\nWrite one possible equation for the volume of the composite figure.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14934\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-107.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 107\" width=\"171\" height=\"199\" \/><\/p>\n<p>Answer:<br \/>\n4 x + 6 y = 13<br \/>\n4 x + 2 y = 1<\/p>\n<p>Question 7.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds the volume of the composite figure. Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14935\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-108.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 108\" width=\"320\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-108.png 320w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-108-300x166.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><\/p>\n<p>Answer:<br \/>\nyes, my friend is correct.<\/p>\n<p>Explanation:<br \/>\nvolume = l x w x h<br \/>\nv = 12 x 2 x 3<br \/>\nv = 72 cubic ft<br \/>\nv = l x w x h<br \/>\nv = 5 x 2 x 5<br \/>\nv = 10 x 5<br \/>\nv = 50 cubic ft.<br \/>\nv = 72 + 50<br \/>\nv = 122 cubic ft.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nThe depth of the swimming pool is 5 feet. How many cubic feet of water can the pool hold?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14936\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-109.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 109\" width=\"195\" height=\"151\" \/><br \/>\nBreak apart the pool into rectangular prisms. Find the dimensions of each prism.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14937\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-110.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 110\" width=\"642\" height=\"438\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-110.png 642w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-110-300x205.png 300w\" sizes=\"(max-width: 642px) 100vw, 642px\" \/><\/p>\n<p>Answer:<br \/>\nso, the cube can hold 1200 cubic feet of water.<\/p>\n<p>Explanation:<br \/>\nvolume of prism A = l x w x h<br \/>\nl = 12 , w = 5 , h = 20<br \/>\nv = 12 x 5 x 20<br \/>\nv = 60 x 20<br \/>\nv = 1200 cubic feet.<br \/>\nvolume of prism B = l x w x h<br \/>\nl = 40 , w = 5 v = 1200<br \/>\n1200 = 40 x 5 x h<br \/>\n1200 = 200 x h<br \/>\n1200 = 200h<br \/>\nh = (1200\/200)<br \/>\nh = 6 ft<br \/>\nvolume of prism C = l x w x h<br \/>\nh = 6, w = 5 , v = 1200<br \/>\n1200 = l x 5 x 6<br \/>\n1200 = l x 30<br \/>\n1200 = 30 l<br \/>\nl = (1200\/30)<br \/>\nl = 40 ft<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 8.<br \/>\nHow many cubic centimeters of wood are needed to make the game piece?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14938\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-112.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 112\" width=\"204\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\nThe game needed to make the game piece = 90 cubic cm.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38627\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.5-1.png\" alt=\"\" width=\"337\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.5-1.png 337w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-13-Understand-Volumes-13.5-1-300x149.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><br \/>\nvolume\u00a0 of prism A= l x w x h<br \/>\nv = 9 x 2 x 3<br \/>\nv = 18 x 3<br \/>\nv = 54 cubic cm<br \/>\nvolume of pridm B= l x w x h<br \/>\nv = 6 x 2 x 3<br \/>\nv = 12 x 3<br \/>\nv = 36 cubic cm.<\/p>\n<p>Question 9.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWhat is the volume of the building surrounding the outdoor courtyard? Explain your method.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14939\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-113.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 113\" width=\"186\" height=\"129\" \/><\/p>\n<p>Answer:<br \/>\nThe building surrounding the outdoor courtyard = 1,008 cubic m<\/p>\n<p>Explanation:<br \/>\nvolume of building surrounding inside\u00a0 = l x w x h<br \/>\nh = 6, w = 6 m , h = 14<br \/>\nv = 6 x 6 x 14<br \/>\nv = 36 x 14<br \/>\nv = 504 cubic m.<br \/>\nThe outdoor courtyard is 2 times the inside courtyard.<br \/>\nv = 504 x 2<br \/>\nv = 1,008 cubic m<\/p>\n<h3><a id=\"Find_Volumes_of_Composite_Figures_Homework_&amp;_Practice_13.5\"><\/a>Find Volumes of Composite Figures Homework &amp; Practice 13.5<\/h3>\n<p>Question 1.<br \/>\nFind the volume of the composite figure.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14940\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-114.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 114\" width=\"161\" height=\"170\" \/><\/p>\n<p>Answer:<br \/>\nvolume of figure 1 = 160 cubic ft.<br \/>\nvolume of figure 2 = 12 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the figure 1( left side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=5 ft , w = 4 ft , h = 8 ft.<br \/>\nvolume = l x w x h<br \/>\nv = 5 x 4 x 8<br \/>\nv = 20 x 8<br \/>\nv = 160 cubic ft.<br \/>\nvolume of the figure 2 (right side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l= 3ft , w = 2 ft , h = 2 ft.<br \/>\nvolume = l x w x h<br \/>\nv = 3 x 2 x 2<br \/>\nv = 6 x 2<br \/>\nv = 12 cubic ft.<\/p>\n<p>Find the volume of the composite figure.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14941\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-115.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 115\" width=\"265\" height=\"116\" \/><\/p>\n<p>Answer:<br \/>\nvolume of figure 1 = 40 cubic in.<br \/>\nvolume of figure 2 = 42 cubic in.<\/p>\n<p>Explanation:<br \/>\nvolume of the figure 1( left side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=10 ft , w = 2 in , h = 2 in.<br \/>\nvolume = l x w x h<br \/>\nv = 10 x 2 x 2<br \/>\nv = 20 x 2<br \/>\nv = 40 cubic in.<br \/>\nvolume of the figure 2 (right side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l= 3in , w = 7 in , h = 2 in.<br \/>\nvolume = l x w x h<br \/>\nv = 3 x 7 x 2<br \/>\nv = 21 x 2<br \/>\nv = 42 cubic in.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14942\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-116.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 116\" width=\"215\" height=\"128\" \/>\\<\/p>\n<p>Answer:<br \/>\nvolume of figure 1 = 25 cubic cm.<br \/>\nvolume of figure 2 = 48 cubic cm.<\/p>\n<p>Explanation:<br \/>\nvolume of the figure 1( top ) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=5 cm , w = 1 cm , h = 5 cm.<br \/>\nvolume = l x w x h<br \/>\nv = 5 x 1 x 5<br \/>\nv = 5 x 5<br \/>\nv = 25 cubic cm.<br \/>\nvolume of the figure 2 (bottom ) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l= 8 cm , w = 6 cm , h = 1 cm.<br \/>\nvolume = l x w x h<br \/>\nv = 8 x 6 x 1<br \/>\nv = 48 x 1<br \/>\nv = 48 cubic cm.<\/p>\n<p>Question 4.<br \/>\n<strong>Structure<\/strong><br \/>\nFind the volume of the composite figure two different ways.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14943\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-117.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 117\" width=\"224\" height=\"128\" \/><\/p>\n<p>Answer:<br \/>\nvolume of figure 1 = 288 cubic ft.<br \/>\nvolume of figure 2 = 60\u00a0 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the figure 1( bottom) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l= 12 ft , w = 6 ft , h = 4 ft.<br \/>\nvolume = l x w x h<br \/>\nv = 12 x 6 x 4<br \/>\nv = 72 x 4<br \/>\nv = 288 cubic ft.<br \/>\nvolume of the figure 2 (top) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l= 5 ft , w = 4 ft , h = 3 ft.<br \/>\nvolume = l x w x h<br \/>\nv = 5 x 4 x 3<br \/>\nv = 20 x 3<br \/>\nv = 60 cubic ft.<\/p>\n<p>Question 5.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nThe height of the garden bed is 2 feet. How many cubic feet of soil are in the garden bed?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14944\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-118.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 118\" width=\"201\" height=\"106\" \/><\/p>\n<p>Answer:<br \/>\nThe soil in the garden bed= 48 cubic feet.<\/p>\n<p>Explanation:<br \/>\nv = l x w x h<br \/>\nwhere l = 16 &#8211; 2 (5)<br \/>\nl = 16 -10 = 6 ft<br \/>\nw = 12 &#8211; 8<br \/>\nw = 4 ft<br \/>\nh = 2 ft given<br \/>\nv = 6 x 4 x 2<br \/>\nv = 24 x 2<br \/>\nv = 48 cubic ft<\/p>\n<p>Question 6.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe dimensions of each step are the same. How many cubic inches of concrete does a worker need to make the staircase?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14945\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-119.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 119\" width=\"188\" height=\"154\" \/><\/p>\n<p>Answer:<br \/>\nThe concrete does a worker need to make the staircase = 10,368 cubic in.<\/p>\n<p>Explanation:<br \/>\nvolume of the figure = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l= 36 in , w = 9 in , h = 8 in.<br \/>\nvolume = l x w x h<br \/>\nv = 36 x 9 x 8<br \/>\nv = 324 x 8<br \/>\nv = 2,592 cubic in.<br \/>\nIn the above-given figure there are\u00a0 4 steps.<br \/>\nv = 2592 x 4<br \/>\nv = 10,368 cubic in<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14946\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-120.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 120\" width=\"122\" height=\"52\" \/><\/p>\n<p>Answer: 4<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14947\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-121.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 121\" width=\"133\" height=\"63\" \/><\/p>\n<p>Answer: 3<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14948\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-122.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 122\" width=\"116\" height=\"62\" \/><\/p>\n<p>Answer: 21\/8<\/p>\n<h3><a id=\"Understand_Volume_Performance_Task_13\"><\/a>Understand Volume Performance Task 13<\/h3>\n<p>Mechanical engineers follow guidelines when designing and installing elevators to make sure passengers are safe and the elevators are wheelchair accessible. Many elevators have heating and air conditioning units attached to them, so it is important to know the volume inside the elevator to keep the air a comfortable temperature.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14949\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-123.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 123\" width=\"220\" height=\"252\" \/><\/p>\n<p>Question 1.<br \/>\nThe inside of the elevator shown is in the shape of a rectangular prism.<br \/>\na. What is the volume of the inside of the elevator?<br \/>\nb. Another elevator has the same height and width. The length of the inside is doubled. How does this affect the volume?<br \/>\nc. Five people ride with their luggage on the elevator. Each person weighs about 200 pounds. The total combined weight of their luggage is about 425 pounds. About how many more pounds can the elevator hold?<\/p>\n<p>Answer:<br \/>\na. The volume of the inside elevator = 240 cubic ft<br \/>\nb. The volume increases.<br \/>\nc.The more pounds the elevator can hold = 1,875 pounds.<\/p>\n<p>Explanation:<br \/>\na. The volume of the inside elevator = l x w x h<br \/>\ngiven that elevator is in the shape of a rectangular prism.<br \/>\nv = 5 x 6 x 8<br \/>\nwhere l = 5 , w = 6 and h = 8<br \/>\nv = 5 x 6 x 8<br \/>\nv = 30 x 8<br \/>\nv = 240 cubic ft.<br \/>\nb. given that if the length is doubled = 2 x 5<br \/>\nl = 10<br \/>\nv = 10 x 6 x 8<br \/>\nv = 60 x 8<br \/>\nv = 480 cubic ft<br \/>\nc. Five people ride with their luggage on the elevator. Each person weighs about 200 pounds. The total combined weight of their luggage is about 425 pounds.<br \/>\n425 + 200<br \/>\n625 pounds.<br \/>\nMaximum capacity = 2500 pounds<br \/>\n2500 &#8211; 625 = 1,875 pounds<\/p>\n<p>Question 2.<br \/>\nThe inside of all new elevators must be wheelchair accessible. The minimum requirements are shown. The inside volume of an older elevator is 144 cubic feet. The base is a square and the height is 9 feet.<br \/>\na. Explain why the older elevator does not meet the wheelchair requirements.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14950\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-125.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 125\" width=\"178\" height=\"216\" \/><br \/>\nb. A new wheelchair-accessible elevator is added to the building. Its height is 9 feet. Find the minimum volume of the new elevator. How does this compare to the volume of the old elevator?<\/p>\n<p>Answer:<br \/>\na. The older elevator does not meet the wheelchair requirements because the elevator is added to the building.<br \/>\nb. The minimum volume of the new elevator = 30 cubic ft<\/p>\n<p>Explanation:<br \/>\na. The older elevator does not meet the wheelchair requirements because the elevator is added to the building.<br \/>\nb. The minimum volume of the new elevator = base x height<br \/>\nh = 6 x 2\/3 = 20\/3 = 6.66<br \/>\n6.66\/2 = 3.33<br \/>\nv = 3.33 x 9<br \/>\nv = 30 cubic ft.<\/p>\n<h3><a id=\"Understand_Volume_Activity\"><\/a>Understand Volume Activity<\/h3>\n<p><strong>Directions:<\/strong><\/p>\n<ol>\n<li>Players take turns rolling a die.<\/li>\n<li>On your turn, move your piece the number of spaces shown on the die.<\/li>\n<li>Find the volume of the rectangular prism.<\/li>\n<li>Cover the volume with a counter. Your turn is over.<\/li>\n<li>The first player to get three in a row, horizontally, vertically, or diagonally, wins!<\/li>\n<\/ol>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-14951\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-126.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 126\" width=\"629\" height=\"617\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-126.png 629w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-126-300x294.png 300w\" sizes=\"(max-width: 629px) 100vw, 629px\" \/><\/p>\n<h3><a id=\"Understand_Volume_Chapter_Practice\"><\/a>Understand Volume Chapter Practice<\/h3>\n<p><strong>13.1 Understand the Concept of Volume<\/strong><\/p>\n<p>Find the volume of the figure.<\/p>\n<p>Question 1.<br \/>\nVolume = ____<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14952\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-127.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 127\" width=\"229\" height=\"97\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the cube = 28 cubic feet.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 7 x 4 x 1<br \/>\nIn the above-given figure l=7 ft, w =4 ft and h = 1ft<br \/>\nvolume = 7 x 4 x 1<br \/>\nvolume = 28 x 1<br \/>\nvolume = 28 cubic ft<\/p>\n<p>Question 2.<br \/>\nVolume = ____<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14953\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-128.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 128\" width=\"105\" height=\"142\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the cube = 9 cubic feet.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 3 x 1 x 3<br \/>\nIn the above-given figure l=3 ft, w =1 ft and h = 3ft<br \/>\nvolume = 3 x 1 x 3<br \/>\nvolume = 3 x 3<br \/>\nvolume = 9 cubic ft<\/p>\n<p>Question 3.<br \/>\nVolume = ____<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14954\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-129.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 129\" width=\"120\" height=\"164\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the cube = 8 cubic in.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 2 x 1 x 4<br \/>\nIn the above-given figure l=2 in, w =1 in and h = 4 in.<br \/>\nvolume = 2 x 1 x 4<br \/>\nvolume = 2 x 4<br \/>\nvolume = 8 cubic in.<\/p>\n<p>Question 4.<br \/>\nVolume = ____<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14955\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-130.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 130\" width=\"206\" height=\"123\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the cube = 18 cubic cm.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 3 x 3 x 2<br \/>\nIn the above-given figure l= 3 cm, w =3cm and h = 2 cm.<br \/>\nvolume = 3 x 3 x 2<br \/>\nvolume = 9 x 2<br \/>\nvolume = 18 cubic cm.<\/p>\n<p>Question 5.<br \/>\nVolume = ____<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14956\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-131.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 131\" width=\"182\" height=\"159\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the cube = 16 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 4 x 1 x 4<br \/>\nIn the above-given figure l= 4 ft, w = 1 ft and h = 4ft.<br \/>\nvolume = 4 x 1 x 4<br \/>\nvolume = 4 x 4<br \/>\nvolume = 16 cubic ft.<\/p>\n<p>Question 6.<br \/>\nVolume = ____<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14957\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-132.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 132\" width=\"193\" height=\"111\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the cube = 16 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 4 x 2 x 2<br \/>\nIn the above-given figure l= 4 ft, w = 2 ft and h = 2ft.<br \/>\nvolume = 4 x 2 x 2<br \/>\nvolume = 8 x 2<br \/>\nvolume = 16 cubic ft.<\/p>\n<p>Question 7.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA container holds 30 of the phone boxes shown, without any gaps or overlaps. What is the volume of the container?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14958\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-133.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 133\" width=\"265\" height=\"131\" \/><\/p>\n<p>Answer:<br \/>\nThe volume of the container = 36 cubic in.<\/p>\n<p>Explanation:<br \/>\nvolume = length x width x height<br \/>\nwhere l = length, w = width and h = height<br \/>\nvolume = 6 x 3 x 2<br \/>\nIn the above-given figure l= 6 in, w = 3 in and h = 2 in.<br \/>\nvolume = 6 x 3 x 2<br \/>\nvolume = 18 x 2<br \/>\nvolume = 36 cubic in.<\/p>\n<p><strong>13.2 Find Volumes of Right Rectangular Prisms<\/strong><\/p>\n<p>Question 8.<br \/>\nVolume =<\/p>\n<p>Question 9.<br \/>\nVolume =___<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14960\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-135.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 135\" width=\"153\" height=\"171\" \/><\/p>\n<p>Answer:<br \/>\nThe Volume of the rectangular prism = 84 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l= 4 ft , w = 3 ft, h = 7 ft .<br \/>\nvolume = l x w x h<br \/>\nv = 4 x 3 x 7<br \/>\nv = 12 x 7<br \/>\nv = 84 cubic ft.<\/p>\n<p>Question 10.<br \/>\nA rectangular prism is made of unit cubes, like the one shown. The prism is 9 centimeters long, 3 centimeters wide, and 5 centimeters tall. What is the volume of the prism?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14961\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-136.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 136\" width=\"66\" height=\"66\" \/><\/p>\n<p>Answer:<br \/>\nThe Volume of the rectangular prism = 135 cubic cm.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l= 9 cm , w = 3 cm, h = 5 cm.<br \/>\nvolume = l x w x h<br \/>\nv = 9 x 3 x 5<br \/>\nv = 27 x 5<br \/>\nv = 135 cubic cm.<\/p>\n<p><strong>13.3 Apply the Volume Formula<\/strong><\/p>\n<p>Find the volume of the rectangular prism.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14962\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-137.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 137\" width=\"181\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\nThe Volume of the rectangular prism = 48 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l= 6 ft , w = 2 ft, h = 4 ft .<br \/>\nvolume = l x w x h<br \/>\nv = 6 x 2 x 4<br \/>\nv = 12 x 4<br \/>\nv = 48 cubic ft.<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14963\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-138.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 138\" width=\"207\" height=\"119\" \/><\/p>\n<p>Answer:<br \/>\nThe Volume of the rectangular prism = 270 cubic cm.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l= 9 cm , w = 6 cm, h = 5 cm .<br \/>\nvolume = l x w x h<br \/>\nv = 9 x 6 x 5<br \/>\nv = 54 x 5<br \/>\nv = 270 cubic cm.<\/p>\n<p>Question 13.<br \/>\nDescartes\u2019s cat cave is a rectangular prism. The cave is 14 inches long, 13 inches wide, and 12 inches tall. What is the volume of the cave?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14964\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-139.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 139\" width=\"149\" height=\"147\" \/><\/p>\n<p>Answer:<br \/>\nThe Volume of the cave = 2,184 cubic in.<\/p>\n<p>Explanation:<br \/>\nvolume of the rectangular prism = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l= 14 in , w = 13 in, h = 12 in .<br \/>\nvolume = l x w x h<br \/>\nv = 14 x 13 x 12<br \/>\nv = 182 x 12<br \/>\nv = 2,184 cubic in.<\/p>\n<p><strong>13.4 Find Unknown Dimensions<\/strong><\/p>\n<p>Find the unknown dimension of the rectangular prism.<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14965\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-140.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 140\" width=\"231\" height=\"100\" \/><\/p>\n<p>Answer:<br \/>\nThe unknown dimensions are l= 9 ft, w= 3 ft,and h = 1 ft.<\/p>\n<p>Explanation:<br \/>\ngiven that area of the base = 27 sq ft<br \/>\narea = l x w<br \/>\n27 = 9 x 3<br \/>\nv = l x w x h<br \/>\n27 = 9 x 3 x h<br \/>\n27 = 27 h<br \/>\nh = (27\/27)<br \/>\nh = 1 ft<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14966\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-141.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 141\" width=\"190\" height=\"174\" \/><\/p>\n<p>Answer:<br \/>\nThe unknown dimensions are l= 6 cm, w= 1 cm,and h = 8 cm.<\/p>\n<p>Explanation:<br \/>\ngiven that area of the base = 48 sq cm.<br \/>\narea = l x w x h<br \/>\n48 = 6 x w x 8<br \/>\nv = l x w x 8<br \/>\n48 = 48 x w<br \/>\n48 = 48 w<br \/>\nw = (48\/48)<br \/>\nw = 1 cm<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14967\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-142.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 142\" width=\"199\" height=\"121\" \/><\/p>\n<p>Answer:<br \/>\nThe unknown dimensions are l=9 in , w= 9 in,and h = 1 in.<\/p>\n<p>Explanation:<br \/>\ngiven that area of the base = 81 sq in.<br \/>\narea = l x w x h<br \/>\n81 = 9 x 9 x h<br \/>\nv = l x w x h<br \/>\n81 = 81 x h<br \/>\n81 = 81 h<br \/>\nh = (81\/81)<br \/>\nh = 1 in<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14968\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-143.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 143\" width=\"266\" height=\"109\" \/><\/p>\n<p>Answer:<br \/>\nThe unknown dimensions are l=1 ft , w= 6 ft ,and h = 3 ft.<\/p>\n<p>Explanation:<br \/>\ngiven that area of the base = 18 sq ft.<br \/>\narea = l x w x h<br \/>\n18 = l x 6 x 3<br \/>\nv = l x w x h<br \/>\n18 = l x 6 x 3<br \/>\n18 = 18 l<br \/>\nl = (18\/18)<br \/>\nh = 1 ft<\/p>\n<p>Question 18.<br \/>\n<strong>Open-Ended<\/strong><br \/>\nA rectangular prism has a volume of 128 cubic feet. The height of the prism is 8 feet. Give one possible set of dimensions for the base.<\/p>\n<p>Answer:<br \/>\nThe dimensions of the base = 16 sq ft.<\/p>\n<p>Explanation:<br \/>\nGiven that volume of rectangular prism = 128 cubic feet.<br \/>\nvolume = base x height<br \/>\nv = 128 given height = 8 ft<br \/>\n128 = b x 8<br \/>\nb = (128\/8)<br \/>\nb = 16 sq ft.<\/p>\n<p>Question 19.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou buy the drawing pad shown. The volume of the drawer is 800 cubic inches. Can the drawing pad lie \ufb02at inside the drawer?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14969\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-144.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 144\" width=\"342\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-144.png 342w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-144-300x171.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><\/p>\n<p>Answer:<br \/>\nYes, the\u00a0 drawing pad will fit\u00a0 inside the drawer.<\/p>\n<p>Explanation:<br \/>\nGiven that volume of drawer = 800 cubic in.<br \/>\nvolume =length x\u00a0 width x height<br \/>\nv = 800 given w = 10 inand h = 8in<br \/>\n800 = l x w x h<br \/>\n800= l x 10 x 8<br \/>\n800 = 80 l<br \/>\nl = (800\/80)<br \/>\nl = 10 in<br \/>\nGiven that base of\u00a0 drawig pad = 10 in.<br \/>\nvolume = base x height<br \/>\ngiven b = 10 in h = 12 in<br \/>\nv = 10 x 12<br \/>\nv= 120 cubic in.<\/p>\n<p><strong>13.5 Find Volumes of Composite Figures<\/strong><\/p>\n<p>Find the volume of the composite figure<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14970\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-145.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 145\" width=\"223\" height=\"147\" \/><\/p>\n<p>Answer:<br \/>\nvolume of figure 1 = 300 cubic ft.<br \/>\nvolume of figure 2 = 480 cubic ft.<\/p>\n<p>Explanation:<br \/>\nvolume of the figure 1( left side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=15 ft , w = 10 ft , h = 2 ft.<br \/>\nvolume = l x w x h<br \/>\nv = 15 x 10 x 2<br \/>\nv = 150 x 2<br \/>\nv = 300 cubic ft.<br \/>\nvolume of the figure 2 (right side) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=6 ft , w = 10 ft , h = 8 ft.<br \/>\nvolume = l x w x h<br \/>\nv = 6 x 10 x 8<br \/>\nv = 60 x 8<br \/>\nv = 480 cubic ft.<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14971\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-13-Understand-Volume-146.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 13 Understand Volume 146\" width=\"251\" height=\"127\" \/><\/p>\n<p>Answer:<br \/>\nvolume of figure 1 = 88 cubic cm.<br \/>\nvolume of figure 2 = 12 cubic cm.<\/p>\n<p>Explanation:<br \/>\nvolume of the figure 1( top) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=11 cm , w = 8 cm , h = 1 cm.<br \/>\nvolume = l x w x h<br \/>\nv = 11 x 8 x 1<br \/>\nv = 88 x 1<br \/>\nv = 88 cubic cm.<br \/>\nvolume of the figure 2 (bottom) = length x width x height<br \/>\nwhere l = length, w= width and h = height<br \/>\ngiven, l=4 cm , w = 3 cm , h = 1 cm.<br \/>\nvolume = l x w x h<br \/>\nv = 4 x 3 x 1<br \/>\nv = 12 x 1<br \/>\nv = 12 cubic cm.<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>The question and answers seen in the above article are prepared as per the latest syllabus. So, the students of the 5th Class can make use of the links and kickstart your preparation. Clarify your doubts by posting the comments in the below comment box. Keep in touch with us to get the Answer Key for all Big Ideas Math Grade 5 Chapters.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A perfect preparation will come to your hand when you have the best source with you. Finding the best source will help you to save your time while preparing and also get a grip on the concept. The only best source to learn all the Grade 5 Chapter 13 Understand Volume is our Big Ideas &#8230; <a title=\"Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-5-chapter-13\/\" aria-label=\"More on Big Ideas Math Answers Grade 5 Chapter 13 Understand Volume\">Read more<\/a><\/p>\n","protected":false},"author":12,"featured_media":89670,"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\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-13-Understand-Volume.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/14907"}],"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=14907"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/14907\/revisions"}],"predecessor-version":[{"id":90256,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/14907\/revisions\/90256"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89670"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=14907"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=14907"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=14907"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}