{"id":167311,"date":"2024-11-15T15:36:54","date_gmt":"2024-11-15T15:36:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=167311"},"modified":"2024-11-15T15:36:56","modified_gmt":"2024-11-15T15:36:56","slug":"the-perimeter-of-a-quarter-circle-is-3-57-cm","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/15\/the-perimeter-of-a-quarter-circle-is-3-57-cm\/","title":{"rendered":"The perimeter of a quarter circle is 3.57 cm."},"content":{"rendered":"\n<p>The perimeter of a quarter circle is 3.57 cm. What is the quarter circles area?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the area of a quarter circle, we need to first understand how the perimeter of a quarter circle relates to its radius. The perimeter of a quarter circle consists of two parts:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Arc length<\/strong>: The curved portion of the quarter circle, which is a quarter of the circumference of the full circle.<\/li>\n\n\n\n<li><strong>Straight edges<\/strong>: These are the two radii of the circle, which form the right-angle sides of the quarter circle.<\/li>\n<\/ol>\n\n\n\n<p>Given that the perimeter of the quarter circle is 3.57 cm, we can break it into its components:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Arc length<\/strong>: This is a quarter of the total circumference of the circle. The formula for the circumference of a full circle is ( C = 2\\pi r ), where ( r ) is the radius. The arc length of the quarter circle is ( \\frac{1}{4} \\times 2\\pi r = \\frac{\\pi r}{2} ).<\/li>\n\n\n\n<li><strong>Straight edges<\/strong>: These are simply the two radii, so their total length is ( 2r ).<\/li>\n<\/ul>\n\n\n\n<p>Thus, the total perimeter ( P ) of the quarter circle is the sum of the arc length and the straight edges:<br>[<br>P = \\frac{\\pi r}{2} + 2r<br>]<br>We are told that the perimeter is 3.57 cm, so:<br>[<br>3.57 = \\frac{\\pi r}{2} + 2r<br>]<br>Now, solve for ( r ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Solve for ( r )<\/h3>\n\n\n\n<p>Rewrite the equation:<br>[<br>3.57 = \\frac{\\pi r}{2} + 2r<br>]<\/p>\n\n\n\n<p>Factor out ( r ):<br>[<br>3.57 = r \\left( \\frac{\\pi}{2} + 2 \\right)<br>]<\/p>\n\n\n\n<p>Numerically approximate ( \\frac{\\pi}{2} + 2 ) (where ( \\pi \\approx 3.14 )):<br>[<br>\\frac{3.14}{2} + 2 = 1.57 + 2 = 3.57<br>]<\/p>\n\n\n\n<p>So the equation simplifies to:<br>[<br>3.57 = r \\times 3.57<br>]<\/p>\n\n\n\n<p>Thus, ( r = 1 ) cm.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Calculate the Area of the Quarter Circle<\/h3>\n\n\n\n<p>The area ( A ) of a quarter circle is given by:<br>[<br>A = \\frac{1}{4} \\pi r^2<br>]<\/p>\n\n\n\n<p>Substitute ( r = 1 ) cm:<br>[<br>A = \\frac{1}{4} \\pi (1)^2 = \\frac{1}{4} \\pi \\approx \\frac{1}{4} \\times 3.14 = 0.785 \\, \\text{cm}^2<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The area of the quarter circle is approximately <strong>0.785 cm\u00b2<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The perimeter of a quarter circle is 3.57 cm. What is the quarter circles area? The Correct Answer and Explanation is: To find the area of a quarter circle, we need to first understand how the perimeter of a quarter circle relates to its radius. The perimeter of a quarter circle consists of two parts: [&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-167311","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167311","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=167311"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167311\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167311"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167311"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167311"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}