{"id":21707,"date":"2016-02-17T22:15:41","date_gmt":"2016-02-17T22:15:41","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=21707"},"modified":"2026-03-25T11:36:56","modified_gmt":"2026-03-25T16:36:56","slug":"how-to-find-the-volume-of-3d-objects","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/how-to-find-the-volume-of-3d-objects\/","title":{"rendered":"How to Calculate the Volume of 3D Objects"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_rRy1A5hX9_c\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_rRy1A5hX9_c\" data-source-videoID=\"rRy1A5hX9_c\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"How to Calculate the Volume of 3D Objects Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"How to Calculate the Volume of 3D Objects\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_rRy1A5hX9_c:hover {cursor:pointer;} img#videoThumbnailImage_rRy1A5hX9_c {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/72-how-to-calculate-the-volume-of-3d-objects-2.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_rRy1A5hX9_c\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_rRy1A5hX9_c\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"How to Calculate the Volume of 3D Objects\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_rRy1A5hX9_c\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_rRy1A5hX9_c\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_rRy1A5hX9_c\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction izK_Function() {\n  var x = document.getElementById(\"izK\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"izK_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"izK\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#The_Volume_of_a_Triangular_Prism\" class=\"smooth-scroll\">The Volume of a Triangular Prism<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Volume_of_a_Cube_or_Rectangular_Prism\" class=\"smooth-scroll\">Volume of a Cube or Rectangular Prism<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Volume_of_a_Sphere\" class=\"smooth-scroll\">Volume of a Sphere<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Volume_of_a_Cone\" class=\"smooth-scroll\">Volume of a Cone<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Frequently_Asked_Questions\" class=\"smooth-scroll\">Frequently Asked Questions<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Volume_of_3D_Objects_Practice_Questions\" class=\"smooth-scroll\">Volume of 3D Objects Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"FAQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"FAQs\">FAQs<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hey, guys! Welcome to this video on the volume of three-dimensional objects.<\/p>\n<p>Let\u2019s start off by defining volume. <strong>Volume<\/strong> is the measurement of how much space a liquid or gas takes up, or how much space a liquid or gas takes up within a given object.<\/p>\n<p>You may not know it, but people use volume every day. Volume is used to calculate the drinking amounts. The amount of water you can hold in a cup is dependent on the volume of the cup. There are several other ways that volume is used.<\/p>\n<p>Now, let\u2019s look at how to calculate the volume of a triangular prism, a rectangular prism, a sphere, and a cone.<\/p>\n<h2><span id=\"The_Volume_of_a_Triangular_Prism\" class=\"m-toc-anchor\"><\/span>The Volume of a Triangular Prism<\/h2>\n<p>\nThe <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/area-and-perimeter-of-a-triangle\/\">area of a triangle<\/a> is \\(A=\\frac{1}{2}bh\\). Essentially, to find to the volume of the triangular prism, you are multiplying the area of the triangle times the length or depth. So, the formula for the volume of a triangular prism would be \\(V=\\frac{1}{2}bhl\\).<br \/>\nLet\u2019s take a look:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-64002\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/triangular-prism.png\" alt=\"triangular prism\" width=\"582.75\" height=\"327.75\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/triangular-prism.png 603w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/triangular-prism-300x178.png 300w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><\/p>\n<p>We have a triangular prism with a height of 8 meters, a base of 13 meters, and a length of 4 meters. All we have to do is plug our numbers into our formula then solve. So we have \\(V=\\frac{1}{2}bhl\\). And once we solve, we get our answer, which is \\(208m^{3}\\). It\u2019s important to know that, when dealing with volume, we will always have cubic units because we are multiplying the units by themselves 3 times.<\/p>\n<h2><span id=\"Volume_of_a_Cube_or_Rectangular_Prism\" class=\"m-toc-anchor\"><\/span>Volume of a Cube or Rectangular Prism<\/h2>\n<p>\nTo find the same <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/volume-and-surface-area-of-a-cube\/\">volume of a cube<\/a> or rectangular prism, you will use the same formula. Just like with the triangular prism, you want to find the area of one side, then multiply it times the length. <\/p>\n<p>However, it\u2019s important to know that the formula you use to find the area of a triangle is not the same formula you use to find the area of a square or a rectangle. The formula for the area of both a square and a rectangle is \\(A=b h\\). So, to find the volume of a cube or rectangular prism, you would find the area of the square or rectangle then multiply it times the length. Which, makes the formula \\(V=bhl\\).<\/p>\n<p>Here is an example:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-63993\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/cube.png\" alt=\"cube\" width=\"582.75\" height=\"327.75\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/cube.png 595w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/cube-300x198.png 300w\" sizes=\"(max-width: 595px) 100vw, 595px\" \/><\/p>\n<p>Here we have a cube, which is a rectangular prism, but all the sides are <a href=\"https:\/\/www.mometrix.com\/academy\/square-root-and-perfect-square\/\"><strong>perfect squares<\/strong><\/a>. Because it\u2019s a cube, we know that all of the sides are the same distance. So all we need to do is multiply 10 times itself 3 times. This gives us 1,000 meters cubed. Let\u2019s try another:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-63997\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/rectangular-prism.png\" alt=\"rectangular prism\" width=\"582.75\" height=\"327.75\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/rectangular-prism.png 657w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/rectangular-prism-300x161.png 300w\" sizes=\"(max-width: 657px) 100vw, 657px\" \/><\/p>\n<p>Here, we have a rectangular prism with sides that are different in distance. We have a base of 12 cm, a height of 8 cm, and a length of 6 cm. Now, all we need to do is plug those numbers into our formula, and once we solve, we get 576 cm cubed.<\/p>\n<h2><span id=\"Volume_of_a_Sphere\" class=\"m-toc-anchor\"><\/span>Volume of a Sphere<\/h2>\n<p>\nNow if you remember the area of a circle is \\(A=\\pi r^{2}\\). That is pi times the radius squared. Well, to find the volume of a sphere you will use a similar formula, but multiply it times \\(\\frac{4}{3}\\) and switching the \\(r^{2}\\) to make it \\(r^{3}\\). Making the formula for the volume of a sphere \\(V=\\frac{4}{3} \\pi r^{3}\\). When you do what is called a proof, to prove that this is the formula, but for now we&#8217;ll just plug the numbers into the given formula.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-63999\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/sphere.png\" alt=\"sphere\" width=\"349.65\" height=\"196.65\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/sphere.png 370w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/sphere-300x285.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><\/p>\n<p>The sphere has a diameter of 20 meters. This is all the information we need to plug in and solve our equation. We are looking for the radius, and we know that the radius is equal to half of the diameter, which means that our radius is equal to 10 meters. When we plug 10 into our formula, and solve, we get 4,188.9 meters cubed.<\/p>\n<h2><span id=\"Volume_of_a_Cone\" class=\"m-toc-anchor\"><\/span>Volume of a Cone<\/h2>\n<p>\nThe formula for <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/volume-and-surface-area-of-a-right-circular-cone\/\">volume of a cone<\/a> is very similar to the formula for the area of a circle. However, there are two things added to the formula.<\/p>\n<p>To find the volume of a cone, you multiply times \\(\\frac{1}{3}\\), and times the height because now you have a height (because now you are working with a three-dimensional shape). This makes the formula for the volume of a cone \\(V=\\frac{1}{3}h\\pi r^{2}\\). Here is an example:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-63991\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/cone.png\" alt=\"cone\" width=\"495.3375\" height=\"278.5875\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/cone.png 373w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/cone-300x254.png 300w\" sizes=\"(max-width: 373px) 100vw, 373px\" \/><\/p>\n<p>Here we can see that we have a height of 5 cm and a radius of 2 cm. Once we plug in all of our numbers, we have \\(V=\\frac{1}{3}(5cm)\\pi (2)^{2}\\). When solved, we have \\(V=20.94cm^{3}\\).<\/p>\n<p>Great job, you guys. Learning new formulas can be hard. The important thing is to keep practicing so that you are able to recognize which formula you need to use and to memorize the formulas. I hope this was helpful. See you next time!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"FAQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Frequently_Asked_Questions\" class=\"m-toc-anchor\"><\/span>Frequently Asked Questions<\/h2>\n<div class=\"faq-list\">\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you find the volume of a triangular prism?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Find the volume of a triangular prism by multiplying the area of the base (the triangle part) by the height of the prism: \\(V = Bh\\).<\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: Find the volume of this triangular prism:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/01\/Volume-of-a-Triangular-Prism-example.svg\" alt=\"A triangular prism with a base of 7 meters, height of 8 meters, and length of 12 meters.\" width=\"335\" height=\"183\" class=\"aligncenter size-full wp-image-286450\"  role=\"img\" \/><\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center; margin-bottom: 0em; line-height: 40px\">\\(V=Bh=\\frac{1}{2} (7)(8)(12)\\) \\(\\:=336 \\mathrm{\\:m}^3\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you find the volume of a cube?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Find the volume of a cube by cubing its side length (\\(V=s^{3}\\)).<\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: What is the volume of a cube with a side length of <span style=\"white-space:nowrap\">7 cm?<\/span><\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center; margin-bottom: 0em\">\\(V = s^{3} = 7^{3} = 343 \\mathrm{\\:cm}^3\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you find the volume of a rectangular prism?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Find the volume of a rectangular prism by multiplying its length times its width times its height (\\(V = lwh\\)).<\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example:  What is the volume of this rectangular prism?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/01\/Volume-of-a-Rectangular-Prism-example.svg\" alt=\"A rectangular prism with labeled dimensions: 3 inches tall, 7 inches wide, and 11 inches long.\" width=\"288\" height=\"177\" class=\"aligncenter size-full wp-image-286453\"  role=\"img\" \/><\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center; margin-bottom: 0em\">\\( V = 3 \\times 7 \\times 11 = 231 \\mathrm{\\:in}^3\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you find the volume of a sphere?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Find the volume of a sphere by cubing its radius and multiplying by \\(\\frac{4}{3}\\). <\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: What is the volume of a sphere with radius 3 cm?<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center; margin-bottom: 0em; line-height: 40px\">\\(V=\\frac{4}{3}\\pi(3)^3=\\frac{4}{3}\\pi(27)\\)\\(\\:=36\\pi \\mathrm{\\:cm}^3 \\approx 113.04 \\mathrm{\\:cm}^3\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you find the volume of a cone?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Find the volume of a cone by multiplying \\(\\frac{1}{3}\\) times the area of the base times the height, or multiplying \\(\\frac{1}{3}\\) times pi (\\(\\pi\\)) times the radius squared times the height: <\/p>\n<p style=\"text-align: center\">\\(V=\\frac{1}{3}Bh\\) or \\(V=\\frac{1}{3}\\pi r^2h\\)<\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: What is the volume of this cone?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/01\/Volume-of-a-Cone-example-1.svg\" alt=\"Diagram of a cone with a height of 9 inches and a base diameter of 4 inches, both measurements labeled.\" width=\"163.35\" height=\"188.65\" class=\"aligncenter size-full wp-image-286459\"  role=\"img\" \/> <\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center; margin-bottom: 0em; line-height: 40px\">\\(V=\\frac{1}{3}\\pi(4)^2(9)\\)\\(\\:=48\\pi \\mathrm{\\:in}^2\\approx 150.72 \\mathrm{\\:in}^2\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Volume_of_3D_Objects_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Volume of 3D Objects Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the volume of this rectangular prism?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/01\/Volume-of-a-Rectangular-Prism-example-2.svg\" alt=\"A rectangular prism with dimensions labeled: 4 cm in height, 5 cm in width, and 11 cm in length.\" width=\"292\" height=\"175.5\" class=\"aligncenter size-full wp-image-286465\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">112 cm<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-1-2\">153 cm<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-1-3\">198 cm<sup>3<\/sup><\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-4\">220 cm<sup>3<\/sup><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The formula for volume of a rectangular prism is:<\/p>\n<p style=\"text-align:center;\">\\(V=lwh\\)<\/p>\n<p>The length (\\(l\\)) is 5 cm, the width (\\(w\\)) is 4 cm, and the height (\\(h\\)) is 11 cm.<\/p>\n<p style=\"text-align:center;\">\\(V=(5)(4)(11)=220 \\mathrm{\\:cm}^3\\)<\/p>\n<p>Therefore, the volume of this rectangular prism is 220 cm<sup>3<\/sup>.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the volume of a sphere with a 9-inch radius?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">972.29 in<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-2-2\">2,513.06 in<sup>3<\/sup><\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-3\">3,052.08 in<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-2-4\">4,179.14 in<sup>3<\/sup><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The correct answer is 3,052.08 in<sup>3<\/sup>. The formula for finding the volume of a sphere is:<\/p>\n<p style=\"text-align:center;\">\\(V=\\frac{4}{3}\\pi r^3\\)<\/p>\n<p>The radius (\\(r\\)) is 9 inches. <\/p>\n<p style=\"text-align:center; line-height: 40px\">\\(V=\\frac{4}{3}\\pi(9)^3=\\frac{4}{3}\\pi(729)\\)\\(\\:=972\\pi \\approx 3,052.08\\mathrm{\\:in}^3\\)<\/p>\n<p>The volume of this sphere is 3,052.08 in<sup>3<\/sup>.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the formula used to find the volume of a cone?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(V=\\pi r^2h\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-2\">\\(V=\\frac{1}{3}\\pi r^2h\\)<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(V=lwh\\)<\/div><div class=\"PQ\"  id=\"PQ-3-4\">\\(V=\\frac{1}{3}lwh\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The general formula for the volume of a cone or pyramid is \\(V=\\frac{1}{3}Bh\\), where \\(B\\) is the area of the base.<\/p>\n<p>Since the base of a cone is a circle and the area of a circle can be found using the formula \\(A=\\pi r^2\\), substitute \\(B\\) with \\(\\pi r^2\\) to get \\(V=\\frac{1}{3}\\pi r^2h\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the volume of this cone?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/01\/Volume-of-a-Cone-example-2.svg\" alt=\"A cone with a height of 12 feet and a base radius of 3 feet is shown in a line drawing.\" width=\"148.5\" height=\"171.5\" class=\"aligncenter size-full wp-image-286462\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">214.17 ft<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-4-2\">339.12 ft<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-4-3\">97.19 ft<sup>3<\/sup><\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-4\">113.04 ft<sup>3<\/sup><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The formula for volume of a cone is \\(V=\\frac{1}{3}\\pi r^2h\\)<\/p>\n<p>The radius (\\(r\\)) is 3 feet and the height is 12 feet.<\/p>\n<p style=\"text-align:center\">\\(V=\\frac{1}{3}\\pi(3)^2(12)=36\\pi \\approx 113.04 \\mathrm{\\:ft}^3\\)<\/p>\n<p>Therefore, the volume of this cone is 113.04 ft<sup>3<\/sup>.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the volume of this triangular prism?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/01\/Volume-of-a-Triangular-Prism-example-2.svg\" alt=\"A triangular prism with a base of 15 cm, height of 7 cm, and length of 21 cm.\" width=\"335\" height=\"183\" class=\"aligncenter size-full wp-image-286468\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">987 ft<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-5-2\">1,791.5 ft<sup>3<\/sup><\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">1,102.5 ft<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-5-4\">5,355 ft<sup>3<\/sup><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The correct answer is 1,102.5 cm<sup>3<\/sup>. The formula for the volume of a triangular prism is \\(V=Bh\\).<\/p>\n<p>\\(B\\) stands for the area of the base, which in this case is a triangle. The formula for area of a triangle is \\(A=\\frac{1}{2}bh\\). This can be substituted for \\(B\\) so the formula now looks like this:<\/p>\n<p style=\"text-align:center;\">\n\\(V=\\frac{1}{2}bh_Th\\)<\/p>\n<p>The height of the triangle has a subscript \\(T\\) so it can be distinguished from the height of the prism. The length of the base (\\(b\\)) is 15 cm. The length of the triangle\u2019s height (\\(h_T\\)) is 7 cm. The length of the prism height (\\(h\\)) is 21 cm.<\/p>\n<p style=\"text-align:center\">\n\\(V=\\frac{1}{2}(15)(7)(21)=1,102.5 \\mathrm{\\:cm}^3\\)<\/p>\n<p>Therefore, the volume of this triangular prism is 1,102.5 cm<sup>3<\/sup>.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/geometry\/\">Return to Geometry Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Geometry Videos<\/p>\n","protected":false},"author":1,"featured_media":91033,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-21707","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-math-advertising-group","7":"page_category-volume-and-surface-area","8":"page_type-video","9":"content_type-practice-questions","10":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/21707","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=21707"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/21707\/revisions"}],"predecessor-version":[{"id":240502,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/21707\/revisions\/240502"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/91033"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=21707"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}