{"id":376,"date":"2022-04-13T10:49:21","date_gmt":"2022-04-13T10:49:21","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=376"},"modified":"2025-01-29T09:23:39","modified_gmt":"2025-01-29T09:23:39","slug":"t-1-introduction-to-surface-area-and-volume","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/t-1-introduction-to-surface-area-and-volume\/","title":{"rendered":"T.1 Introduction to surface area and volume"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>ntroduction to surface area and volume<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-cc38c3564cde6a3e0a261c272b57b7bc\" style=\"color:#74008b;text-transform:capitalize\"><strong>key notes :<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-c658e5ffe196c54f99daef1708dd0ed7\" style=\"color:#000060\"><strong>Surface Area<\/strong>:<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Definition<\/strong>: Surface area is the total area of all the surfaces (faces) of a 3D object.<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Units<\/strong>: Measured in square units (e.g., cm\u00b2, m\u00b2).<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-5b74bac970466f3f07b0aa9a0b11e6e4\" style=\"color:#000060\"><strong>Formulae<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Cube<\/strong>: 6a<sup>2<\/sup> (where &#8216;a&#8217; is the length of one side).<\/li>\n\n\n\n<li><strong>Rectangular Prism<\/strong>: 2lw + 2lh + 2wh (where &#8216;l&#8217; is length, &#8216;w&#8217; is width, and &#8216;h&#8217; is height).<\/li>\n\n\n\n<li><strong>Cylinder<\/strong>: 2\u03c0r<sup>2<\/sup> + 2\u03c0rh (where &#8216;r&#8217; is the radius and &#8216;h&#8217; is the height).<\/li>\n\n\n\n<li><strong>Sphere<\/strong>: 4\u03c0r<sup>2<\/sup> (where &#8216;r&#8217; is the radius).<\/li>\n\n\n\n<li><strong>Cone<\/strong>: \u03c0r (r+l) (where &#8216;r&#8217; is the radius and &#8216;l&#8217; is the slant height).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-b0d5a42927bf18155d5fcef3526ee34e\" style=\"color:#000060\"><strong>Volume<\/strong>:<\/h3>\n\n\n\n<p class=\"has-large-font-size\"><strong>Definition<\/strong>: Volume is the amount of space occupied by a 3D object.<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Units<\/strong>: Measured in cubic units (e.g., cm\u00b3, m\u00b3).<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-5b74bac970466f3f07b0aa9a0b11e6e4\" style=\"color:#000060\"><strong>Formulae<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Cube<\/strong>: a<sup>3 <\/sup>(where &#8216;a&#8217; is the side length).<\/li>\n\n\n\n<li><strong>Rectangular Prism<\/strong>: l \u00d7 w \u00d7 h (where &#8216;l&#8217; is length, &#8216;w&#8217; is width, and &#8216;h&#8217; is height).<\/li>\n\n\n\n<li><strong>Cylinder<\/strong>: \u03c0r<sup>2<\/sup>h (where &#8216;r&#8217; is the radius and &#8216;h&#8217; is the height).<\/li>\n\n\n\n<li><strong>Sphere<\/strong>: 4\/3 \u03c0r<sup>3<\/sup> (where &#8216;r&#8217; is the radius).<\/li>\n\n\n\n<li><strong>Cone<\/strong>: 1\/3 \u03c0r<sup>2<\/sup>h (where &#8216;r&#8217; is the radius and &#8216;h&#8217; is the height).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-f5e7e7f6ac43b8f9d007836937aab839\" style=\"color:#000060\"><strong>Relation Between Surface Area and Volume<\/strong>:<\/h3>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Surface area and volume are both essential in understanding the size and shape of an object.<\/li>\n\n\n\n<li>While surface area refers to the outer covering, volume deals with the internal space.<\/li>\n\n\n\n<li>In certain cases, like in optimization problems, there&#8217;s a relationship where increasing surface area leads to an increase in volume (e.g., in packing or maximizing efficiency).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-848d63adf673c68901a5c49622a9e7e8\" style=\"color:#000060\"><strong>Real-Life Applications<\/strong>:<\/h3>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Surface Area<\/strong>: Important in cases like determining the amount of material needed to cover an object (paint, wrapping paper, etc.).<\/li>\n\n\n\n<li><strong>Volume<\/strong>: Useful for calculating the capacity of containers (like swimming pools, water tanks, etc.) or the amount of space an object occupies.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-c977cdcf53574225fb63e32f811b1c93\" style=\"color:#000060\"><strong>Conceptual Understanding<\/strong>:<\/h3>\n\n\n\n<p class=\"has-large-font-size\">Understanding the geometric properties of shapes and how dimensions affect surface area and volume is fundamental to solving real-world problems in various fields, including architecture, engineering, and design.<\/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:#bcf9e2\"><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-771a824863627ce1eac5207b9e7797db\" style=\"color:#b00012\"><strong>What is the surface area?<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/image.png\" alt=\"\" class=\"wp-image-4104\"\/><\/figure><\/div>\n\n\n<p>______ square metres.<\/p>\n<\/div><\/div>\n\n\n\n<p>Each face of the cube is a square with sides that are 9 metres long.<\/p>\n\n\n\n<p>Find the area of one face:<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/image-1.png\" alt=\"\" class=\"wp-image-4105\"\/><\/figure><\/div>\n\n\n<p>area=side . side<\/p>\n\n\n\n<p>      =9 . 9<\/p>\n\n\n\n<p>       =81<\/p>\n\n\n\n<p>The area of each face is 81 square metres. There are 6 faces. Multiply:<\/p>\n\n\n\n<p>surface area=6 . 81<\/p>\n\n\n\n<p>         =486<\/p>\n\n\n\n<p>The surface area of the cube is 486 square metres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#b1e4fb\"><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-ccf99c0628c4b07d80a5678076b149e1\" style=\"color:#b00012\"><strong>What is the volume?<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/image-2.png\" alt=\"\" class=\"wp-image-4107\"\/><\/figure><\/div>\n\n\n<p>&nbsp;&#8212;&#8212;cubic millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<p>Find the length, width, and height of the rectangular prism.<\/p>\n\n\n\n<p>length: 6 mm<br>width: 9 mm<br>height: 4 mm<\/p>\n\n\n\n<p>Use these numbers in the formula.<\/p>\n\n\n\n<p>volume=length . width . height<\/p>\n\n\n\n<p>            =6 . 9 . 4<\/p>\n\n\n\n<p>            =216<\/p>\n\n\n\n<p>The volume is 216 cubic millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f2b6e2\"><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-ccf99c0628c4b07d80a5678076b149e1\" style=\"color:#b00012\"><strong>What is the volume?<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/image-3.png\" alt=\"\" class=\"wp-image-4111\"\/><\/figure><\/div>\n\n\n<p>&#8212;&#8212;cubic millimetres.<\/p>\n<\/div><\/div>\n\n\n\n<p>Each side of the cube is 4 millimetres long. Use the number 4 in the formula.<\/p>\n\n\n\n<p>volume=side . side . side<\/p>\n\n\n\n<p>      =4 .4 . 4<\/p>\n\n\n\n<p>       =64<\/p>\n\n\n\n<p>The volume is 64 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\/84551\/148\/349\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-132.png\" alt=\"\" class=\"wp-image-7393\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-132.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-132-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-132-150x150.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\/84615\/716\/871\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-151.png\" alt=\"\" class=\"wp-image-7394\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-151.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-151-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-151-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>ntroduction to surface area and volume key notes : Surface Area: Definition: Surface area is the total area of all the surfaces (faces) of a 3D object. Units: Measured in square units (e.g., cm\u00b2, m\u00b2). Formulae: Volume: Definition: Volume is the amount of space occupied by a 3D object. Units: Measured in cubic units (e.g.,<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/t-1-introduction-to-surface-area-and-volume\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.1 Introduction to surface area and volume&#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-376","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/376","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=376"}],"version-history":[{"count":15,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/376\/revisions"}],"predecessor-version":[{"id":17479,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/376\/revisions\/17479"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=376"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}