{"id":461,"date":"2022-04-12T10:38:56","date_gmt":"2022-04-12T10:38:56","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=461"},"modified":"2025-11-10T09:37:56","modified_gmt":"2025-11-10T09:37:56","slug":"w-11-perimeter-area-and-volume-changes-in-scale","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/w-11-perimeter-area-and-volume-changes-in-scale\/","title":{"rendered":"W.11 Perimeter, area and volume: changes in scale"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Perimeter, area and volume: changes in scale<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-09eb8d27d0d70f35bd20b1cf47293f11\" style=\"color:#74008b\"><strong>Key Notes :<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39Meaning of Scale<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Scale<\/strong> means enlarging (making bigger) or reducing (making smaller) a shape while keeping the same proportions.<\/p>\n\n\n\n<p>When dimensions (length, width, height) of a figure are multiplied by a <strong>scale factor<\/strong>, its perimeter, area, and volume also change.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong> <strong>\ud83d\udd39<\/strong>Effect of Scale Factor on Perimeter, Area, and Volume<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\ud83d\udc49 Suppose the <strong>scale factor = k<\/strong><br>(Every length is multiplied by <strong>k<\/strong>)<\/p>\n\n\n\n<p><strong>Perimeter (1-D Measurement)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Perimeter is directly proportional to the scale factor.<\/li>\n\n\n\n<li>New Perimeter = k \u00d7 Original Perimeter<\/li>\n<\/ul>\n\n\n\n<p><strong>Area (2-D Measurement)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Area is proportional to the square of the scale factor.<\/li>\n\n\n\n<li>New Area = k\u00b2 \u00d7 Original Area<\/li>\n<\/ul>\n\n\n\n<p><strong>Volume (3-D Measurement)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Volume is proportional to the cube of the scale factor.<\/li>\n\n\n\n<li>New Volume = k\u00b3 \u00d7 Original Volume<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39 Examples<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Example 1: Perimeter<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A square has side = 5 cm.<\/li>\n\n\n\n<li>Scale factor = 3.<\/li>\n\n\n\n<li>New side = 5 \u00d7 3 = 15 cm.<\/li>\n\n\n\n<li>Original Perimeter = 4 \u00d7 5 = 20 cm.<\/li>\n\n\n\n<li>New Perimeter = 3 \u00d7 20 = 60 cm. \u2705<\/li>\n<\/ul>\n\n\n\n<p><strong>Example 2: Area<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Rectangle = 6 cm \u00d7 4 cm.<\/li>\n\n\n\n<li>Scale factor = 2.<\/li>\n\n\n\n<li>New dimensions = 12 cm \u00d7 8 cm.<\/li>\n\n\n\n<li>Original Area = 6 \u00d7 4 = 24 cm\u00b2.<\/li>\n\n\n\n<li>New Area = 2\u00b2 \u00d7 24 = 4 \u00d7 24 = 96 cm\u00b2. \u2705<\/li>\n<\/ul>\n\n\n\n<p><strong>Example 3: Volume<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cube with side = 2 cm.<\/li>\n\n\n\n<li>Scale factor = 3.<\/li>\n\n\n\n<li>New side = 6 cm.<\/li>\n\n\n\n<li>Original Volume = 2\u00b3 = 8 cm\u00b3.<\/li>\n\n\n\n<li>New Volume = 3\u00b3 \u00d7 8 = 27 \u00d7 8 = 216 cm\u00b3. \u2705<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39Key Points to Remember<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Perimeter \u2192 multiplies by k<\/strong><\/li>\n\n\n\n<li><strong>Area \u2192 multiplies by k\u00b2<\/strong><\/li>\n\n\n\n<li><strong>Volume \u2192 multiplies by k\u00b3<\/strong><\/li>\n\n\n\n<li>As shapes grow larger, <strong>area and volume grow much faster<\/strong> than perimeter.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39 Real-Life Applications<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Maps (scale drawings).<\/li>\n\n\n\n<li>Models of buildings, cars, and machines.<\/li>\n\n\n\n<li>Enlarging\/reducing images in printing or designing.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\u2705 <strong>Summary:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p> When a figure is enlarged or reduced by a <strong>scale factor (k):<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Perimeter \u00d7 k<\/li>\n\n\n\n<li>Area \u00d7 k\u00b2<\/li>\n\n\n\n<li>Volume \u00d7 k\u00b3<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-huge-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-normal-font-size\" style=\"background-color:#f8f9d1\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>\u25b6\ufe0f Look at this rectangular prism:<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-10-2.png\" alt=\"\" class=\"wp-image-5309\" style=\"aspect-ratio:1;width:309px;height:auto\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-10-2.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-10-2-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-10-2-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-10-2-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>If the width is doubled, then which of the following statements about its volume will be true?<\/strong><\/p>\n\n\n\n<p id=\"block-a5c88a3a-8dcc-4f7c-9349-95d59600d4f9\">Look at this rectangular prism:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The new volume will be 3 times the old volume.<\/li>\n\n\n\n<li>The new volume will be 2 times the old volume.<\/li>\n\n\n\n<li>The new volume will be 12 of the old volume.<\/li>\n\n\n\n<li>The new volume will be 4 times the old volume.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>You can solve this problem without using the measurements given in the diagram.<\/p>\n\n\n\n<p>The original rectangular prism had this volume:<\/p>\n\n\n\n<p><em>V<\/em>&nbsp;=&nbsp;<em>lwh<\/em><\/p>\n\n\n\n<p>The new rectangular prism will have 2 times the width. Since the original width was w, the new width will be 2w. Calculate the volume:<\/p>\n\n\n\n<p>V = l(2w)h<\/p>\n\n\n\n<p>= 2lwh<\/p>\n\n\n\n<p>Divide the new volume by the original volume and simplify.<\/p>\n\n\n\n<p>new volume\/ original volume = 2lwh \/ <em>lwh<\/em><\/p>\n\n\n\n<p>= 2<\/p>\n\n\n\n<p>The new volume will be 2 times the old volume.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-normal-font-size\" style=\"background-color:#d6ddfc\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>\u25b6\ufe0f Look at this cube:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-11-3.png\" alt=\"\" class=\"wp-image-5310\" style=\"aspect-ratio:1;width:277px;height:auto\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-11-3.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-11-3-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-11-3-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-11-3-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>If the side lengths are tripled, then which of the following statements about its surface area will be true?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The new surface area will be 3 times the old surface area<\/li>\n\n\n\n<li>The new surface area will be 1\/4 of the old surface area<\/li>\n\n\n\n<li>The new surface area will be 27 times the old surface area.<\/li>\n\n\n\n<li>The new surface area will be 9 times the old surface area<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>You can solve this problem without using the measurements given in the diagram.<\/p>\n\n\n\n<p>The original cube had this surface area:<\/p>\n\n\n\n<p><em>S<\/em>&nbsp;= 6<em>s<\/em><sup>2<\/sup><\/p>\n\n\n\n<p>The new cube will have sides that are 3 times as long. Since the original side lengths were s, the new side lengths will be 3s. Calculate the surface area:<\/p>\n\n\n\n<p>S = 6(3s)<sup>2<\/sup><\/p>\n\n\n\n<p>= 6 \u00b7 9s<sup>2<\/sup><\/p>\n\n\n\n<p>= 54s<sup>2<\/sup><\/p>\n\n\n\n<p>Divide the new surface area by the original surface area and simplify.<\/p>\n\n\n\n<p>new surface area \/ original surface area = 54s<sup>2<\/sup> \/ 6s<sup>2<\/sup><\/p>\n\n\n\n<p>= 9 <\/p>\n\n\n\n<p>The new surface area will be 9 times the old surface area.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-normal-font-size\" style=\"background-color:#edd3f6\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>\u25b6\ufe0f Look at this square:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-12-2.png\" alt=\"\" class=\"wp-image-5311\" style=\"aspect-ratio:1;width:292px;height:auto\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-12-2.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-12-2-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-12-2-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-12-2-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>If the side lengths are doubled, then which of the following statements about its perimeter will be true?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The new perimeter will be 2 times the old perimeter.<\/li>\n\n\n\n<li>The new perimeter will be 3 times the old perimeter.<\/li>\n\n\n\n<li>The new perimeter will be 1\/2 of the old perimeter.<\/li>\n\n\n\n<li>The new perimeter will be 4 times the old perimeter.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>You can solve this problem without using the measurements given in the diagram.<\/p>\n\n\n\n<p>The original square had this perimeter:<\/p>\n\n\n\n<p><em>P<\/em>&nbsp;= 4<em>s<\/em><\/p>\n\n\n\n<p>The new square will have sides that are 2 times as long. Since the original side lengths were s, the new side lengths will be 2s. Calculate the perimeter:<\/p>\n\n\n\n<p>P = 4(2s)<\/p>\n\n\n\n<p>= 8s<\/p>\n\n\n\n<p>Divide the new perimeter by the original perimeter and simplify.<\/p>\n\n\n\n<p>new perimeter \/ original perimeter = 8s\/4s<\/p>\n\n\n\n<p>= 2<\/p>\n\n\n\n<p>The new perimeter will be 2 times the old perimeter.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#cb1414\">Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/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\/101667\/349\/549\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-135.png\" alt=\"\" class=\"wp-image-6902\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-135.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-135-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-135-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-135-400x400.png 400w\" 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\/101668\/465\/878\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-137.png\" alt=\"\" class=\"wp-image-6903\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-137.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-137-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-137-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-137-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Perimeter, area and volume: changes in scale Key Notes : \ud83d\udd39Meaning of Scale Scale means enlarging (making bigger) or reducing (making smaller) a shape while keeping the same proportions. When dimensions (length, width, height) of a figure are multiplied by a scale factor, its perimeter, area, and volume also change. \ud83d\udd39Effect of Scale Factor on<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/w-11-perimeter-area-and-volume-changes-in-scale\/\">Continue reading <span class=\"screen-reader-text\">&#8220;W.11 Perimeter, area and volume: changes in scale&#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,"footnotes":""},"class_list":["post-461","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/461","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=461"}],"version-history":[{"count":22,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/461\/revisions"}],"predecessor-version":[{"id":17577,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/461\/revisions\/17577"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=461"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}