{"id":145932,"date":"2024-09-30T05:04:08","date_gmt":"2024-09-30T05:04:08","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=145932"},"modified":"2024-09-30T05:04:11","modified_gmt":"2024-09-30T05:04:11","slug":"here-is-a-circle-and-a-scaled-copy-of-the-circle-with-a-scale-factor-of-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/30\/here-is-a-circle-and-a-scaled-copy-of-the-circle-with-a-scale-factor-of-2\/","title":{"rendered":"Here is a circle and a scaled copy of the circle with a scale factor of 2"},"content":{"rendered":"\n<p>Here is a circle and a scaled copy of the circle with a scale factor of <code>2<\/code>.<br>How does the circumference of the scaled copy compare to the circumference of the original circle?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The image shows two concentric circles: a smaller one in blue and a larger one in green. Based on the description, the larger circle is a scaled copy of the smaller one with a scale factor of 2.<\/p>\n\n\n\n<p>The formula for the circumference of a circle is:<\/p>\n\n\n\n<p>[<br>C = 2\\pi r<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( C ) is the circumference.<\/li>\n\n\n\n<li>( r ) is the radius of the circle.<\/li>\n<\/ul>\n\n\n\n<p>In the original circle, the radius is ( r ), and the circumference is:<\/p>\n\n\n\n<p>[<br>C_{\\text{original}} = 2\\pi r<br>]<\/p>\n\n\n\n<p>When the circle is scaled by a factor of 2, the radius of the scaled circle becomes ( 2r ). The new circumference is:<\/p>\n\n\n\n<p>[<br>C_{\\text{scaled}} = 2\\pi (2r) = 4\\pi r<br>]<\/p>\n\n\n\n<p>Thus, the circumference of the scaled copy is ( 4\\pi r ), which is <strong>twice<\/strong> the original circumference. Therefore, the circumference of the scaled circle is doubled compared to the original circle.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Detailed Explanation<\/h3>\n\n\n\n<p>Scaling a geometric shape by a factor ( k ) increases all linear dimensions by ( k ). In the case of a circle, the radius, which is a linear dimension, scales by ( k = 2 ). Since the circumference of a circle is directly proportional to its radius, doubling the radius also doubles the circumference. This means the new circle has a circumference twice that of the original circle.<\/p>\n\n\n\n<p>Although the area of a circle grows by the square of the scale factor (i.e., ( k^2 )), the circumference scales linearly with the radius. Thus, when the radius is doubled, the circumference also doubles.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is a circle and a scaled copy of the circle with a scale factor of 2.How does the circumference of the scaled copy compare to the circumference of the original circle? The Correct Answer and Explanation is : The image shows two concentric circles: a smaller one in blue and a larger one in [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-145932","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145932","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=145932"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145932\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=145932"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=145932"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=145932"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}