{"id":382,"date":"2022-04-13T10:50:10","date_gmt":"2022-04-13T10:50:10","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=382"},"modified":"2025-01-24T11:20:18","modified_gmt":"2025-01-24T11:20:18","slug":"t-4-volume-of-prisms-and-cylinders","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/t-4-volume-of-prisms-and-cylinders\/","title":{"rendered":"T.4 Volume of prisms and cylinders"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Volume of prisms and cylinders<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-203290aba75681a4fb07a0852f132b50\" style=\"color:#74008b;text-transform:capitalize\">key notes :<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-8f128aeb348cf6102088f65c13b29261\" style=\"color:#000060\"><strong>Definition of Volume<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Volume is the amount of space occupied by a 3D object.<\/li>\n\n\n\n<li>It is measured in cubic units (e.g., cm\u00b3, m\u00b3).<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-b73487d1439f98e38627dfd53b4d2c42\" style=\"color:#000060\"><strong>Volume of a Prism<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>A prism is a solid with two identical bases and rectangular lateral faces.<\/li>\n\n\n\n<li>Formula:<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>V = B \u00d7 h<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">where:<\/p>\n\n\n\n<p class=\"has-large-font-size\">B = Area of the base<\/p>\n\n\n\n<p class=\"has-large-font-size\">h = Height of the prism<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-1b747959f08a7b07495a8bd41a6d3e98\" style=\"color:#000060\"><strong>Types of Prisms:<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Rectangular Prism:<\/strong> V = l \u00d7 w \u00d7 h<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Triangular Prism:<\/strong> V = 12 \u00d7 b \u00d7 h<sub>base<\/sub> \u00d7 h<sub>prism<\/sub><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-f6101770ff1593f84011e2a81030242f\" style=\"color:#000060\"><strong>Volume of a Cylinder<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\">A cylinder is a 3D shape with two circular bases and a curved surface.<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Formula<\/strong>: <\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>V = \u03c0r<sup>2<\/sup>h <\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">where:<\/p>\n\n\n\n<p class=\"has-large-font-size\">r = Radius of the circular base<\/p>\n\n\n\n<p class=\"has-large-font-size\">h = Height of the cylinder<\/p>\n\n\n\n<p class=\"has-large-font-size\">\u03c0 \u2248 3.1416<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-d2cd203d12c1c08b08534f6d4ef8a237\" style=\"color:#000060\"><strong>Comparing Prisms and Cylinders<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Both follow the general volume formula: <strong>Base Area \u00d7 Height<\/strong><\/li>\n\n\n\n<li>A prism has polygonal bases, while a cylinder has circular bases.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-79b96efe841d1714a350f505b7bad18b\" style=\"color:#000060\"><strong>Key Problem-Solving Steps<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Identify the shape (prism or cylinder).<\/li>\n\n\n\n<li>Find the base area (BBB) using appropriate formulas.<\/li>\n\n\n\n<li>Multiply the base area by the height (hhh).<\/li>\n\n\n\n<li>Use proper units and round off answers if necessary.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-1ec4fe1a88aa8443bf6b6df0989263ea\" style=\"color:#000060\"><strong>Example Problems<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\">Find the volume of a rectangular prism with dimensions 5 cm \u00d7 4 cm \u00d7 10 cm. <\/p>\n\n\n\n<p class=\"has-large-font-size\">V = 5 \u00d7 4 \u00d7 10 = 200&nbsp;cm3<\/p>\n\n\n\n<p class=\"has-large-font-size\">Calculate the volume of a cylinder with radius 7 cm and height 12 cm. <\/p>\n\n\n\n<p class=\"has-large-font-size\">V = \u03c0 (7<sup>2<\/sup>)(12) = \u03c0(49)(12) = 588\u03c0 \u2248 1847.52&nbsp;cm<sup>3<\/sup><\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#e2fbba\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-b1b6d7094a9a417da97b2fb6e6ed5074\" style=\"color:#b00012\">What is the volume?<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-11-1.png\" alt=\"\" class=\"wp-image-10826\" style=\"width:340px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-11-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-11-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-11-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>_______ cubic millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<p>Each side of the cube is 8 millimetres long. Use the number 8 in the formula.<\/p>\n\n\n\n<p>volume=side . side . side<\/p>\n\n\n\n<p>= 8 . 8 . 8<\/p>\n\n\n\n<p>= 512<\/p>\n\n\n\n<p>The volume is 512 cubic millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#baf4ca\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>What is the volume of this cylinder?<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-aceb31132f26cef0978b33376694437e\" style=\"color:#b00012\"><strong>Use&nbsp;\u200b\ud835\udf0b&nbsp;\u2248 3.14 and round your answer to the nearest hundredth.<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-12.png\" alt=\"\" class=\"wp-image-10827\" style=\"width:312px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-12.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-12-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-12-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>______ cubic millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<p>Find the radius and height of the cylinder.<\/p>\n\n\n\n<p>radius = 1\/2 . diameter=1\/2 . 2 = 1<\/p>\n\n\n\n<p>height = 2<\/p>\n\n\n\n<p>Use these numbers in the volume formula. Use 3.14 for&nbsp;\u200b\ud835\udf0b.<\/p>\n\n\n\n<p>volume = \ud835\udf0br<sup>2<\/sup> h<\/p>\n\n\n\n<p>             \u2248&nbsp;3.14 . 1 . 1 . 2<\/p>\n\n\n\n<p>\u2248 6.28<\/p>\n\n\n\n<p>The volume of the cylinder is about 6.28 cubic millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#cce7fd\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>What is the volume of this cylinder?<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-aceb31132f26cef0978b33376694437e\" style=\"color:#b00012\"><strong>Use&nbsp;\u200b\ud835\udf0b&nbsp;\u2248 3.14 and round your answer to the nearest hundredth.<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-13.png\" alt=\"\" class=\"wp-image-10828\" style=\"width:285px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-13.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-13-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-13-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>_______ cubic millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<p>Find the radius and height of the cylinder.<\/p>\n\n\n\n<p>radius = 1\/2 . diameter =1\/2 . 2 = 1<\/p>\n\n\n\n<p>height = 2<\/p>\n\n\n\n<p>Use these numbers in the volume formula. Use 3.14 for&nbsp;\u200b\ud835\udf0b.<\/p>\n\n\n\n<p>volume = \ud835\udf0br<sup>2<\/sup> h<\/p>\n\n\n\n<p>             \u2248&nbsp;3.14 . 1 . 1 . 2<\/p>\n\n\n\n<p>\u2248 6.28<\/p>\n\n\n\n<p>The volume of the cylinder is about 6.28 cubic millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/84642\/163\/647\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-135.png\" alt=\"\" class=\"wp-image-7403\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-135.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-135-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-135-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/84772\/681\/387\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-154.png\" alt=\"\" class=\"wp-image-7404\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-154.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-154-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-154-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Volume of prisms and cylinders key notes : Definition of Volume Volume of a Prism V = B \u00d7 h where: B = Area of the base h = Height of the prism Types of Prisms: Rectangular Prism: V = l \u00d7 w \u00d7 h Triangular Prism: V = 12 \u00d7 b \u00d7 hbase \u00d7<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/t-4-volume-of-prisms-and-cylinders\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.4 Volume of prisms and cylinders&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-382","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/382","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=382"}],"version-history":[{"count":13,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/382\/revisions"}],"predecessor-version":[{"id":17468,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/382\/revisions\/17468"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=382"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}