{"id":156420,"date":"2022-03-26T01:44:13","date_gmt":"2022-03-25T20:14:13","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/volume-of-a-prism\/"},"modified":"2024-12-13T12:50:41","modified_gmt":"2024-12-13T07:20:41","slug":"volume-of-a-prism","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/volume-of-a-prism\/","title":{"rendered":"Volume of a Prism"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/volume-of-a-prism\/#Volume_of_Prism_Formula\" title=\"Volume of Prism Formula\">Volume of Prism Formula<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/volume-of-a-prism\/#What_is_Prism\" title=\"What is Prism?\">What is Prism?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/volume-of-a-prism\/#Different_Types_of_Prism\" title=\"Different Types of Prism\">Different Types of Prism<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/volume-of-a-prism\/#What_is_Volume_of_a_Prism\" title=\"What is Volume of a Prism?\">What is Volume of a Prism?<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/volume-of-a-prism\/#Therefore_Volume_General_Formula_it_is_Represented_as\" title=\"Therefore Volume General Formula it is Represented as,\">Therefore Volume General Formula it is Represented as,<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/volume-of-a-prism\/#Volume_of_Prism_Formula-2\" title=\"Volume of Prism Formula\">Volume of Prism Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/volume-of-a-prism\/#Solved_Examples\" title=\"Solved Examples\">Solved Examples<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Volume_of_Prism_Formula\"><\/span>Volume of Prism Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Volume of a Prism.<\/p>\n<p>The volume of a prism is the product of the area of the base and the height of the prism. The volume of a prism is given by the formula:<\/p>\n<p>Volume = (area of base) \u00d7 (height)<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156419 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/volume-of-a-prism.jpg\" alt=\"Volume of a Prism\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/volume-of-a-prism.jpg?v=1648239251 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/volume-of-a-prism-300x212.jpg?v=1648239251 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"What_is_Prism\"><\/span><b>What is Prism?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">A three-dimensional solid shape having its base and top as identical polygons and side faces as parallelograms are called a prism. <\/span><\/p>\n<p style=\"font-weight: 400;\"><b>A Prism is a Solid Object with:<\/b><\/p>\n<ul style=\"font-weight: 400;\">\n<li>Identical base and top which are parallel to each other.<\/li>\n<li>The side faces are flat and parallelogram<\/li>\n<li>No curve sides<\/li>\n<li>And the same cross-section along with its length.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Different_Types_of_Prism\"><\/span><b>Different Types of Prism<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"font-weight: 400;\">A prism is a solid three-dimensional geometric figure with two similar ends and all flat sides. The prism is named after the shape of its base, hence a prism with a triangular base is called a &#8220;triangular prism\u201d. So the different types of prisms are given their names on the basis of their cross-sectional figure formed.<\/p>\n<p style=\"font-weight: 400;\"><b>Types of Prisms are:<\/b><\/p>\n<ul style=\"font-weight: 400;\">\n<li>Triangular Prism<\/li>\n<li>Square Prism<\/li>\n<li>Cube<\/li>\n<li>Cuboid or rectangular Prism<\/li>\n<li>Pentagonal Prism<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"What_is_Volume_of_a_Prism\"><\/span><b>What is Volume of a Prism?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"font-weight: 400;\">As the prism is a 3D solid object it has both the surface area and volume.<\/p>\n<p style=\"font-weight: 400;\">The volume of a 3D prism is defined as the total space occupied by that object.<\/p>\n<p style=\"font-weight: 400;\">To calculate the volume of a prism, you just have to calculate the area of its base and multiply it by its height.<\/p>\n<p style=\"font-weight: 400;\">(image will be uploaded soon)<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Therefore_Volume_General_Formula_it_is_Represented_as\"><\/span>Therefore Volume General Formula it is Represented as,<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<table>\n<tbody>\n<tr>\n<td><b>Volume of a Prism (V)<\/b> = Base Area \u00d7 Length<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"font-weight: 400;\">The volume of a three-dimensional prism is represented as cubic units.<\/p>\n<p style=\"font-weight: 400;\">Here&#8217;s how to calculate the volume of a variety of prisms.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Volume_of_Prism_Formula-2\"><\/span><b>Volume of Prism Formula<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"font-weight: 400;\">Different prisms have different volumes. So the formula to calculate the volume of different Prisms are:<\/p>\n<ul>\n<li>Triangular Prism<\/li>\n<\/ul>\n<p style=\"font-weight: 400;\">A prism having its base and top as identical triangles and the lateral faces are rectangles is called a triangular prism.<\/p>\n<p style=\"font-weight: 400;\">A triangular prism has<\/p>\n<ul style=\"font-weight: 400;\">\n<li>5 faces<\/li>\n<li>6 vertices and<\/li>\n<li>9 edges<\/li>\n<\/ul>\n<p style=\"font-weight: 400;\">(image will be uploaded soon)<\/p>\n<table>\n<tbody>\n<tr>\n<td><b>Volume of Triangular Prism<\/b> = (<\/p>\n<p><span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;block&quot;&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mn&gt;2&lt;\/mn&gt;&lt;\/mfrac&gt;&lt;\/math&gt;\">1212<\/span><\/p>\n<p>) a x b x h<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"font-weight: 400;\">Where,<\/p>\n<p style=\"font-weight: 400;\">a = Apothem length of a triangular prism<\/p>\n<p style=\"font-weight: 400;\">b = Base length of a triangular prism<\/p>\n<p style=\"font-weight: 400;\">h = height of a triangular prism<\/p>\n<ul>\n<li>Square Prism<\/li>\n<\/ul>\n<p style=\"font-weight: 400;\">In a square prism, the base and top are congruent squares and the lateral faces are rectangles<\/p>\n<p style=\"font-weight: 400;\">A square prism has<\/p>\n<ul style=\"font-weight: 400;\">\n<li>6 faces<\/li>\n<li>8 vertices and<\/li>\n<li>12 edges<\/li>\n<\/ul>\n<p style=\"font-weight: 400;\">(image will be uploaded soon)<\/p>\n<table>\n<tbody>\n<tr>\n<td><b>Volume of a Square Prism <\/b>= l x b x h<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"font-weight: 400;\">Where<\/p>\n<p style=\"font-weight: 400;\">l = length of a square prism<\/p>\n<p style=\"font-weight: 400;\">b = Base of a square prism<\/p>\n<p style=\"font-weight: 400;\">h = height of a square prism<\/p>\n<ul>\n<li>Cube<\/li>\n<\/ul>\n<p style=\"font-weight: 400;\">If a square prism has all of its faces as identical squares, then it is called a cube prism.<\/p>\n<p style=\"font-weight: 400;\">A cubic prism or a cube has<\/p>\n<ul style=\"font-weight: 400;\">\n<li>6 faces<\/li>\n<li>8 vertices and<\/li>\n<li>12 edges<\/li>\n<\/ul>\n<p style=\"font-weight: 400;\">(image will be uploaded soon)<\/p>\n<table>\n<tbody>\n<tr>\n<td><b>Volume of a Cube Prism<\/b> =<\/p>\n<p><span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;block&quot;&gt;&lt;msup&gt;&lt;mi&gt;a&lt;\/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn&gt;3&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/msup&gt;&lt;\/math&gt;\">a3a3<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"font-weight: 400;\">Where<\/p>\n<p style=\"font-weight: 400;\">a = edges of a cube prism( because l = w = h = a)<\/p>\n<ul>\n<li>Cuboid or Rectangular Prism<\/li>\n<\/ul>\n<p style=\"font-weight: 400;\">If the base and top of the prism are identical rectangles, then it is a rectangular prism or a cuboid.<\/p>\n<p style=\"font-weight: 400;\">A cuboid prism has<\/p>\n<ul style=\"font-weight: 400;\">\n<li>6 faces<\/li>\n<li>8 vertices and<\/li>\n<li>12 edges<\/li>\n<\/ul>\n<p style=\"font-weight: 400;\">(image will be uploaded soon)<\/p>\n<table>\n<tbody>\n<tr>\n<td><b>Volume of Rectangular Prism<\/b> = l x b x h<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"font-weight: 400;\">Where<\/p>\n<p style=\"font-weight: 400;\">l = length of a rectangular prism<\/p>\n<p style=\"font-weight: 400;\">b = Base of a rectangular prism<\/p>\n<p style=\"font-weight: 400;\">h = height of a rectangular prism<\/p>\n<ul>\n<li>Pentagonal Prism<\/li>\n<\/ul>\n<p style=\"font-weight: 400;\">If the base and top of a prism are pentagons, then it is called a pentagonal prism.<\/p>\n<p style=\"font-weight: 400;\">A pentagonal prism has<\/p>\n<ul style=\"font-weight: 400;\">\n<li>7 faces<\/li>\n<li>10 vertices and<\/li>\n<li>15 edges<\/li>\n<\/ul>\n<p style=\"font-weight: 400;\">(image will be uploaded soon)<\/p>\n<table>\n<tbody>\n<tr>\n<td><b>Volume of Pentagonal Prism<\/b> = (<\/p>\n<p><span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;block&quot;&gt;&lt;mfrac&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;mn&gt;2&lt;\/mn&gt;&lt;\/mfrac&gt;&lt;\/math&gt;\">5252<\/span><\/p>\n<p>) a x b x h<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"font-weight: 400;\">Where,<\/p>\n<p style=\"font-weight: 400;\">a \u2013 Apothem length of the pentagonal prism.<\/p>\n<p style=\"font-weight: 400;\">b \u2013 Base length of the pentagonal prism.<\/p>\n<p style=\"font-weight: 400;\">h \u2013 Height of the pentagonal prism<\/p>\n<ul>\n<li>Hexagonal Prism<\/li>\n<\/ul>\n<p style=\"font-weight: 400;\">A hexagonal prism is a prism with six rectangular faces and top and base as hexagonal.<\/p>\n<p style=\"font-weight: 400;\">A hexagonal prism has<\/p>\n<ul style=\"font-weight: 400;\">\n<li>8 faces<\/li>\n<li>12 vertices and<\/li>\n<li>18 edges<\/li>\n<\/ul>\n<p style=\"font-weight: 400;\">(image will be uploaded soon)<\/p>\n<table>\n<tbody>\n<tr>\n<td><b>Volume of Hexagonal Prism<\/b> = 3 x a x b x h<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"font-weight: 400;\">Where<\/p>\n<p style=\"font-weight: 400;\">a \u2013 Apothem length of the hexagonal prism.<\/p>\n<p style=\"font-weight: 400;\">b \u2013 Base length of the hexagonal prism.<\/p>\n<p style=\"font-weight: 400;\">h \u2013 Height of the hexagonal prism.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Solved_Examples\"><\/span><b>Solved Examples<\/b><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"font-weight: 400;\">Example 1 : Find the volume of the triangular prism given below.<\/p>\n<p style=\"font-weight: 400;\">(image will be uploaded soon)<\/p>\n<p style=\"font-weight: 400;\">Solution:<\/p>\n<p style=\"font-weight: 400;\">Given that a = Apothem length of a triangular prism = 9cm<\/p>\n<p style=\"font-weight: 400;\">b = Base length of a triangular prism = 12 cm<\/p>\n<p style=\"font-weight: 400;\">h = height of a triangular prism = 18cm<\/p>\n<p style=\"font-weight: 400;\">We have, Volume of triangular prism = (<\/p>\n<p><span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;block&quot;&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mn&gt;2&lt;\/mn&gt;&lt;\/mfrac&gt;&lt;\/math&gt;\">1212<\/span><\/p>\n<p style=\"font-weight: 400;\">) a x b x h<\/p>\n<p style=\"font-weight: 400;\">=<\/p>\n<p><span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;block&quot;&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mn&gt;2&lt;\/mn&gt;&lt;\/mfrac&gt;&lt;\/math&gt;\">1212<\/span><\/p>\n<p style=\"font-weight: 400;\">x 9 x 12 x 18<\/p>\n<p style=\"font-weight: 400;\">= 972<\/p>\n<p><span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;block&quot;&gt;&lt;mi&gt;c&lt;\/mi&gt;&lt;msup&gt;&lt;mi&gt;m&lt;\/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn&gt;3&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/msup&gt;&lt;\/math&gt;\">cm3cm3<\/span><\/p>\n<p style=\"font-weight: 400;\">So the volume of the triangular prism is 972 cubic centimeter.<\/p>\n<p style=\"font-weight: 400;\">Example 2: Find the volume of rectangular prism given below.<\/p>\n<p style=\"font-weight: 400;\">(image will be uploaded soon)<\/p>\n<p style=\"font-weight: 400;\">Solution:<\/p>\n<p style=\"font-weight: 400;\">Given that: l = length of a rectangular prism = 9cm<\/p>\n<p style=\"font-weight: 400;\">b = Base of a rectangular prism = 7cm<\/p>\n<p style=\"font-weight: 400;\">h = height of a rectangular prism = 13cm<\/p>\n<p style=\"font-weight: 400;\">We have, Volume of Rectangular Prism = l x b x h<\/p>\n<p style=\"font-weight: 400;\">                      = 9 x 7 x 13<\/p>\n<p style=\"font-weight: 400;\">          = 819<\/p>\n<p><span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;block&quot;&gt;&lt;mi&gt;c&lt;\/mi&gt;&lt;msup&gt;&lt;mi&gt;m&lt;\/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn&gt;3&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/msup&gt;&lt;\/math&gt;\">cm3cm3<\/span><\/p>\n<p style=\"font-weight: 400;\">Therefore the volume of rectangular prism is 819 cubic centimeters.<\/p>\n<p>Volume of a Prism.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Volume of Prism Formula Volume of a Prism. The volume of a prism is the product of the area of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Volume of a Prism","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn Volume of a Prism topic of Maths by experts on infinitylearn.com. Register free for online tutoring session to clear your doubts.","custom_permalink":"maths\/volume-of-a-prism\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Volume of a Prism - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn Volume of a Prism topic of Maths by experts on infinitylearn.com. 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