{"id":90484,"date":"2021-08-26T15:04:14","date_gmt":"2021-08-26T20:04:14","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=90484"},"modified":"2026-03-26T09:44:38","modified_gmt":"2026-03-26T14:44:38","slug":"volume-and-surface-area-of-a-rectangular-prism","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/volume-and-surface-area-of-a-rectangular-prism\/","title":{"rendered":"Volume and Surface Area of a Rectangular Prism"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_sEVdsoEOH2c\" 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_sEVdsoEOH2c\" data-source-videoID=\"sEVdsoEOH2c\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Volume and Surface Area of a Rectangular Prism Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Volume and Surface Area of a Rectangular Prism\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_sEVdsoEOH2c:hover {cursor:pointer;} img#videoThumbnailImage_sEVdsoEOH2c {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/1876-thumb-final-v2-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_sEVdsoEOH2c\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_sEVdsoEOH2c\" 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\",\"Volume and Surface Area of a Rectangular Prism\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_sEVdsoEOH2c\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_sEVdsoEOH2c\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_sEVdsoEOH2c\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction Tpj_Function() {\n  var x = document.getElementById(\"Tpj\");\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=\"Tpj_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=\"Tpj\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Volume_and_Surface_Area_of_a_Rectangular_Prism_Practice_Questions\" class=\"smooth-scroll\">Volume and Surface Area of a Rectangular Prism 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=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label><a href=\"https:\/\/www.mometrix.com\/academy\/cube-rectangular-prism-calculator\/\" target=\"none\" style=\"margin: 0 auto;\"><span class=\"accordion_calculator_button\">Calculator<\/span><\/a><\/p>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello! Today we\u2019re going to examine the most common of 3D figures, the rectangular prism, also known as a rectangular solid. Like with most 3D figures, we can calculate the volume and the surface area by using relatively simple formulas. But before we do that, we need to define a few terms. <\/p>\n<p>A <strong>rectangular prism<\/strong>, or rectangular solid, is a six-sided object where each side, also called a face, is a rectangle. It has twelve edges and eight vertices and all of its angles are right angles.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/01\/rect-prism-4@300-scaled.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\"  role=\"img\" \/><\/p>\n<p>An important measure of a rectangular prism is the volume. The <strong>volume of a prism<\/strong> or any other 3D object is a measure of how much space it takes up. We measure this in cubic units, such as cubic inches or cubic centimeters. It\u2019s easy to picture this with a rectangular prism. Imagine that we have a bunch of little cubes that are 1 centimeter tall, 1 centimeter wide, and 1 centimeter long. Each one of these cubes is 1 cubic centimeter, which can also be written like this \\(1\\text{ cm}^3\\). This is our unit of measure. Notice that it is in cubic units. Volume is a 3-dimensional measure so it\u2019s always in cubic units. <\/p>\n<p>Now let\u2019s build a rectangular prism out of the little centimeter cubes. We\u2019ll start with the lowest level and arrange them in a \\(5\\times 3\\) rectangle. At this point, we\u2019ve used 15 cubes to make our shape, and we have successfully created a rectangular prism. <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/01\/stack-1@300.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\"  role=\"img\" \/><\/p>\n<p>But we can also stack the cubes to make it a little taller. If we place another layer of cubes on top of the first layer, we\u2019ll have a \\(5\\times{3}\\times{2}\\) rectangular prism. And since we used 15 more little cubes to make the second layer, we\u2019re up to 30 cubes altogether. So the volume of our prism is \\(30\\times \\text{ cm}^3\\). <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/01\/stack-2@300.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\"  role=\"img\" \/><\/p>\n<p>Notice that if we multiply the dimensions of our \\(5\\times{3}\\times{2}\\) cube, we get our volume! That\u2019s because the formula for the volume of a rectangular prism is the product of the dimensions: <\/p>\n<div class=\"examplesentence\">\\(V=lwh\\)<\/div>\n<p>\n&nbsp;<br \/>\nSo in this case, our volume \\(V=5\\times{3}\\times{2}=30\\). But let\u2019s not forget our units! Technically our prism measures <span style=\"font-size: 90%\">\\(5\\text{ cm}\\times{3}\\text{ cm}\\times{2\\text{ cm}}. 5\\times{3}\\times{2}=30\\)<\/span> and <span style=\"font-size: 90%\">\\(\\text{cm} \\times \\text{cm} \\times \\text{cm}=\\text{cm}^3\\)<\/span><\/p>\n<p>An example of a real-world volume problem is if we needed to pour a foundation for a rectangular building \u2013 we need to measure the area of each side of the building to find out how much concrete we need to prepare. So if we had to pour a foundation that is <span style=\"font-size: 85%\">\\(42.5\\text{ m long}\\times{20\\text{ m wide}}\\times{0.4\\text{ m deep}}\\)<\/span>  (this is height), we can use those dimensions to find the volume of our foundation by plugging that into our formula: <\/p>\n<div class=\"examplesentence\">\\(V=lwh\\)<\/div>\n<p>\n&nbsp;<\/p>\n<div class=\"examplesentence\">\\(V=42.5\\text{ m}\\times 20\\text{ m}\\times 0.4\\text{ m}\\)\\(=340\\text{ m}^{3}\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow let\u2019s work on finding the surface area. <strong>Surface area<\/strong> has \u201carea\u201d in the name because it really is a measure of area and therefore is a 2-dimensional measure. Its units are therefore square units, like \\(\\text{cm}^2\\). It\u2019s well-named because we\u2019re literally finding the area of the outer surface of the object. So all we need to do is find the area of each face, or side, of our rectangular prism and then add all the sides together. If we take a look at the prism we built from our little centimeter cubes, we can see the squares on the faces. Each one of these squares is a square centimeter. <\/p>\n<p>We can see three of the six faces from this angle. The top face has 15 squares. The left face has 6, and the right face has 10. If we add those up, we have 31 square centimeters that we can see. But since this is a rectangular prism, we know that the sides we can\u2019t see are the same size as the ones we can. The bottom is the same size as the top. The back left is the same size as the front right, and the back right is the same size as the front left. That means that the area of the sides we can&#8217;t see also totals 31 square centimeters. Therefore our total surface area is \\(31\\text{ cm}^2+31\\text{ cm}^2\\) for a total of \\(62\\text{ cm}^2\\). <\/p>\n<p>This problem lets us see the square centimeters, but most surface area problems won\u2019t show us the squares. We\u2019ll just know the dimensions of the rectangular prism, like this: <\/p>\n<p style=\"text-align: center;\"<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-90508\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Volume-and-Surface-Area-of-Rectangular-Prisms-3.png\" alt=\"image of cubed prism 10m by 5m by 4m.\" width=\"600\" height=\"600\" \/>\n<p>Here we can see our prism is 10 meters long by 5 meters wide by 4 meters high. The corresponding edges on the opposite sides will be the same since this is a rectangular prism. The find the surface area, I can use the surface area formula for rectangular prisms: <\/p>\n<div class=\"examplesentence\">\\(SA=2lw+2lh+2wh\\)<\/div>\n<p>\n&nbsp;<br \/>\nThis formula will give us the surface area if we plug in our length, width, and height. <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/01\/whl@300.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\"  role=\"img\" \/><\/p>\n<p>Don\u2019t be confused about which sides are the length, width, and height. Depending on how the prism is oriented on the page, it might appear the 10 m is the length but it really could be the width or the height. It doesn\u2019t matter! But for our purposes, let\u2019s say 10 m is the length, and 5 m  is the width, and 4 m is the height. When we substitute all that in it looks like this: <\/p>\n<div class=\"examplesentence\"><span style=\"font-size: 85%\">\\(SA=2(10\\text{ m})(5\\text{ m})+2(10\\text{ m})(4\\text{ m})\\)\\(+2(5\\text{ m})(4\\text{ m})\\)<\/span><\/div>\n<p>\n&nbsp;<br \/>\nNotice that we left the units in when we substituted. Now when we evaluate each term, we get that the surface area is equal to: <\/p>\n<div class=\"examplesentence\">\\(SA=100\\text{ m}^{2}+80\\text{ m}^2+40\\text{ m}^2\\)<\/div>\n<p>\n&nbsp;<br \/>\nNotice that our units ended up being square units, which is what we need for the surface area. Finally, we just add the terms together to get that our surface area is equal to 220 square meters.<\/p>\n<div class=\"examplesentence\">\\(SA=220\\text{ m}^2\\)<\/div>\n<p>\n&nbsp;<br \/>\nNot too difficult, but it\u2019s worth the time to take a moment to look at what that formula is really doing: <\/p>\n<div class=\"examplesentence\">\\(SA=2lw+2lh+2wh\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe first term, \\(2lw\\), is double the length times the width. This is calculating the area of the bottom and the top of the rectangular prism. The 2 is there to double the area of either one of the sides. The middle term, \\(2lh\\), is double the length times the height. In other words, the front and back sides of the prism. The final term, \\(2wh\\), is double the width times the height. In other words, the left and right sides of the prism. <\/p>\n<p>So the formula is simply finding the area of all 6 sides of the prism 2 at a time. That means that if we ever forget the formula, we can simply find the area of each side individually and add them all up. It takes a bit longer but it totally works. <\/p>\n<p>I hope this video on the surface area and volume of rectangular prisms was helpful. Thanks for watching, and happy studying!<\/p>\n<p>For more help, check out our <a class=\"ylist\" target=\"_blank\" rel=\"noopener noreferrer\" href=\"https:\/\/www.mometrix.com\/academy\/cube-rectangular-prism-calculator\/\">rectangular prism calculator<\/a>!<\/p>\n<ul class=\"citelist\">\n<li><a href=\"https:\/\/www.mathopenref.com\/face.html\"target=\"_blank\">\u201cDefinition of the Math Word Face.\u201d n.d.<\/a><\/li>\n<li><a href=\"https:\/\/www.mathopenref.com\/prism.html \"target=\"_blank\">\u201cPrism Definition &#8211; Math Open Reference.\u201d n.d.<\/a><\/li>\n<li><a href=\"https:\/\/www.mathsisfun.com\/geometry\/cuboids-rectangular-prisms.html\"target=\"_blank\">\u201cCuboids, Rectangular Prisms and Cubes.\u201d n.d.<\/a><\/li>\n<\/ul>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Volume_and_Surface_Area_of_a_Rectangular_Prism_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Volume and Surface Area of a Rectangular Prism 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 \/>\nDetermine the surface area of the rectangular prism. <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Rectangular-Prism-Volume-and-Surface-Area-Example-1.svg\" alt=\"A rectangular prism with dimensions labeled: 7 feet tall, 9 feet wide, and 13 feet long.\" width=\"318.4\" height=\"248.8\" class=\"aligncenter size-full wp-image-287330\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">524 ft<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-1-2\">524 ft<sup>2<\/sup><\/div><div class=\"PQ\"  id=\"PQ-1-3\">542 ft<sup>3<\/sup><\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-4\">542 ft<sup>2<\/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>Rectangular prisms have six faces. Add the areas of the six faces in order to calculate the surface area.<\/p>\n<p>This can be done by using the following formula:<\/p>\n<p style=\"text-align: center;\">\\(SA=2lw+2lh+2wh\\)<\/p>\n<p>Plug in 13 for \\(l\\), 7 for \\(w\\), and 9 for \\(h\\).<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(SA=2(13)(7)+2(13)(9)+2(7)(9)\\)\\(\\:=182+234+126=542\\text{ ft}^2\\)<\/p>\n<p>Since we are calculating an area measurement, the units are squared.<\/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 \/>\nCalculate the volume of the rectangular prism. Round the answer to the nearest whole number. <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Rectangular-Prism-Volume-and-Surface-Area-Example-2.svg\" alt=\"A rectangular box with labeled dimensions: width 6.3 meters, height 7.6 meters, and depth 6.1 meters.\" width=\"284.8\" height=\"227.84\" class=\"aligncenter size-full wp-image-287333\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\">292 m<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-2-2\">224 m<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-2-3\">252 m<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-2-4\">254 m<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 volume of the rectangular prism is found using the formula \\(V=lwh\\).<\/p>\n<p>When the length, width, and height are multiplied, the formula becomes:<\/p>\n<p style=\"text-align: center\">\\(V=6.1\\times6.3\\times7.6\\)<\/p>\n<p>This simplifies to 292.068, which becomes 292 m<sup>3<\/sup> when rounded to the nearest whole number.<\/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 \/>\nFind the volume and surface area of the rectangular prism. <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Rectangular-Prism-Volume-and-Surface-Area-Example-3.svg\" alt=\"A rectangular prism with labeled dimensions: 7 cm length, 5 cm width, and 3 cm height.\" width=\"331.2\" height=\"204\" class=\"aligncenter size-full wp-image-287336\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(SA=152\\text{ cm}^2\\)<br>\r\n\\(V=125\\text{ cm}^3\\)<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\(SA=210\\text{ cm}^2\\)<br>\r\n\\(V=105\\text{ cm}^3\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-3\">\\(SA=142\\text{ cm}^2\\)<br>\r\n\\(V=105\\text{ cm}^3\\)<\/div><div class=\"PQ\"  id=\"PQ-3-4\">\\(SA=142\\text{ cm}^2\\)<br>\r\n\\(V=111\\text{ cm}^3\\)<\/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 surface area is calculated using the following formula:<\/p>\n<p style=\"text-align: center\">\\(SA=2lw+2lh+2wh\\)<\/p>\n<p>Plug in 7 for \\(l\\), 5 for \\(w\\), and 3 for \\(h\\).<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\(SA=2(7)(5)+2(7)(3)+2(5)(3)\\)\\(\\:=70+42+30=142\\text{ cm}^3\\)<\/p>\n<p>The volume is calculated by multiplying the length and width and height <span style=\"white-space:nowrap\">(\\(V=lwh\\))<\/span>. When the three dimensions are multiplied, the formula becomes:<\/p>\n<p style=\"text-align: center\">\\(V=7\\times5\\times3\\)<\/p>\n<p>This simplifies to 105 cm<sup>3<\/sup>.<\/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 \/>\nDrea works for a company that installs swimming pools. What will the volume of the pool be if Drea fills the pool to the 4 meter mark?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Rectangular-Prism-Volume-and-Surface-Area-Example-4.svg\" alt=\"A rectangular prism with labeled dimensions: length 31.5 meters, width 9 meters, and height 5 meters.\" width=\"418.4\" height=\"204\" class=\"aligncenter size-full wp-image-287339\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-4-1\">\\(V=1{,}134\\text{ m}^3\\)<\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\(V=2{,}134\\text{ m}^3\\)<\/div><div class=\"PQ\"  id=\"PQ-4-3\">\\(V=1{,}166\\text{ m}^3\\)<\/div><div class=\"PQ\"  id=\"PQ-4-4\">\\(V=1{,}417.5\\text{ m}^3\\)<\/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 volume of the pool can be found by multiplying the length, width, and height <span style=\"white-space:nowrap\">(\\(V=lwh\\))<\/span>.<\/p>\n<p>If the pool is filled to the 4 meter mark, the formula becomes \\(V=31.5\\times9\\times4\\), which simplifies to \\(V=1{,}134\\text{ m}^3\\).<\/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 \/>\nGeorge built a fish tank that connects two tanks with a middle section. This allows fish to swim back and forth between the chambers. How much water can the entire fish tank hold?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Rectangular-Prism-Volume-and-Surface-Area-Example-5.svg\" alt=\"Two cubes, each 4 ft wide and 3 ft tall, are connected by a 1 ft x 1 ft rectangular tunnel; the tunnel is 2 ft long and positioned 1 ft above the base.\" width=\"626.4\" height=\"227.2\" class=\"aligncenter size-full wp-image-287327\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">70 ft<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-5-2\">71 ft<sup>3<\/sup><\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">74 ft<sup>3<\/sup><\/div><div class=\"PQ\"  id=\"PQ-5-4\">78 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>Volume is calculated as \\(V=lwh\\). The fish tank is made up of three rectangular prisms. Add the volumes of the three prisms.<\/p>\n<ul>\n<li style=\"margin-bottom: 10px\">Left Prism: \\(V=lwh\\) becomes \\(V=4\\times3\\times3=36\\text{ ft}^3\\)<\/li>\n<li style=\"margin-bottom: 10px\">Right Prism: \\(V=lwh\\) becomes \\(V=4\\times3\\times3=36\\text{ ft}^3\\)<\/li>\n<li>Small Middle Prism: \\(V=lwh\\) becomes \\(V=2\\times1\\times1=2\\text{ ft}^3\\)<\/li>\n<\/ul>\n<p>The sum of the volumes of all three prisms is:<\/p>\n<p style=\"text-align: center\">\\(36\\text{ ft}^3+36\\text{ ft}^3+2\\text{ ft}^3=74\\text{ ft}^3\\)<\/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":22,"featured_media":100807,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-90484","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-volume-and-surface-area","7":"page_type-video","8":"content_type-practice-questions","9":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/90484","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\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=90484"}],"version-history":[{"count":7,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/90484\/revisions"}],"predecessor-version":[{"id":240835,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/90484\/revisions\/240835"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/100807"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=90484"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}