{"id":184,"date":"2022-04-13T08:39:04","date_gmt":"2022-04-13T08:39:04","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=184"},"modified":"2025-02-12T11:34:15","modified_gmt":"2025-02-12T11:34:15","slug":"k-4-volume-of-prisms-and-cylinders","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/k-4-volume-of-prisms-and-cylinders\/","title":{"rendered":"K.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-28d136ae4331e7eb05ec8e1cb71ebcde\" style=\"color:#74008b\">key notes :<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-06b45295197b918f0bde9826b6a3cd0a\" style=\"color:#000060\"><strong>Understanding Volume<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\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<p class=\"has-large-font-size\">A prism is a 3D shape with two identical, parallel bases and rectangular sides.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-cc89462af07b0bc298d883d1e0b5c07c\" style=\"color:#000060\"><strong>Formula<\/strong>: <\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>Volume = Base\u00a0Area \u00d7 Height<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-0ef52dea35d4010a72a05d44c1f2fc6d\" style=\"color:#000060\">Types of prisms:<\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Rectangular prism<\/strong>:<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>V = l \u00d7 w \u00d7 h<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Triangular prism<\/strong>: <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>V = 1\/2 \u00d7 Base \u00d7 Height \u00d7 Prism\u00a0Height<\/strong><\/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 has circular bases and a curved surface.<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Formula<\/strong>: V=\u03c0r2hV = \\pi r^2 hV=\u03c0r2h where:<\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>r = radius of the base<\/li>\n\n\n\n<li>h = height of the cylinder<\/li>\n\n\n\n<li>\u03c0\u22483.14 or 22\/7<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-42d444a58cb3eb1648d8bf5e30d7e5ad\" style=\"color:#000060\"><strong>Key Concepts<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Base area<\/strong>: The area of the shape forming the base of the prism or cylinder.<\/li>\n\n\n\n<li><strong>Height<\/strong>: The perpendicular distance between the bases.<\/li>\n\n\n\n<li><strong>Units<\/strong>: Always use cubic units for volume (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-72bc4fe2c9111338294411036d5a4277\" style=\"color:#000060\"><strong>Real-Life Applications<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Measuring the capacity of tanks, pipes, and boxes.<\/li>\n\n\n\n<li>Calculating the amount of material needed for construction.<\/li>\n\n\n\n<li>Understanding storage space in packaging.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" 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 decoding=\"async\" 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\"\/><\/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 decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-12.png\" alt=\"\" class=\"wp-image-10827\" style=\"width:312px;height:auto\"\/><\/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>             \u22486.28<\/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 decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-13.png\" alt=\"\" class=\"wp-image-10828\" style=\"width:285px;height:auto\"\/><\/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>             \u22486.28<\/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\/86043\/396\/923\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-135.png\" alt=\"\" class=\"wp-image-7403\"\/><\/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\/86043\/165\/962\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-154.png\" alt=\"\" class=\"wp-image-7404\"\/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Volume of prisms and cylinders key notes : Understanding Volume Volume of a Prism A prism is a 3D shape with two identical, parallel bases and rectangular sides. Formula: Volume = Base\u00a0Area \u00d7 Height Types of prisms: V = l \u00d7 w \u00d7 h V = 1\/2 \u00d7 Base \u00d7 Height \u00d7 Prism\u00a0Height Volume of<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/k-4-volume-of-prisms-and-cylinders\/\">Continue reading <span class=\"screen-reader-text\">&#8220;K.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-184","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/184","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=184"}],"version-history":[{"count":20,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/184\/revisions"}],"predecessor-version":[{"id":16524,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/184\/revisions\/16524"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=184"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}