{"id":224831,"date":"2025-06-03T14:04:56","date_gmt":"2025-06-03T14:04:56","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224831"},"modified":"2025-06-03T14:04:58","modified_gmt":"2025-06-03T14:04:58","slug":"the-perimeter-of-a-quarter-circle-is-3-57-cm-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/the-perimeter-of-a-quarter-circle-is-3-57-cm-2\/","title":{"rendered":"The perimeter of a quarter circle is 3.57 cm"},"content":{"rendered":"\n

The perimeter of a quarter circle is 3.57 cm. What is the quarter circles area<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To find the area of a quarter circle<\/strong> given its perimeter<\/strong>, we need to first understand the formula for the perimeter of a quarter circle and use it to find the radius<\/strong>, then use the radius to compute the area<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Step 1: Understand the Perimeter Formula<\/strong><\/h3>\n\n\n\n

The perimeter<\/strong> PP of a quarter circle includes:<\/p>\n\n\n\n

    \n
  • One-quarter of the circumference of a full circle: 14\u22c52\u03c0r=\u03c0r2\\frac{1}{4} \\cdot 2\\pi r = \\frac{\\pi r}{2}<\/li>\n\n\n\n
  • Two straight sides: the radius and another radius<\/li>\n<\/ul>\n\n\n\n

    So the formula for perimeter is: P=\u03c0r2+2rP = \\frac{\\pi r}{2} + 2r<\/p>\n\n\n\n

    We are told that the perimeter is 3.57 cm: \u03c0r2+2r=3.57\\frac{\\pi r}{2} + 2r = 3.57<\/p>\n\n\n\n

    \n\n\n\n

    Step 2: Solve for rr<\/strong><\/h3>\n\n\n\n

    Use \u03c0\u22483.1416\\pi \\approx 3.1416: 3.1416r2+2r=3.57\\frac{3.1416 r}{2} + 2r = 3.57 1.5708r+2r=3.571.5708r + 2r = 3.57 3.5708r=3.573.5708r = 3.57 r\u22483.573.5708\u22481.0\u2009cmr \\approx \\frac{3.57}{3.5708} \\approx 1.0 \\, \\text{cm}<\/p>\n\n\n\n

    \n\n\n\n

    Step 3: Use the Radius to Find the Area<\/strong><\/h3>\n\n\n\n

    The area AA of a full circle is: A=\u03c0r2A = \\pi r^2<\/p>\n\n\n\n

    So the area of a quarter circle<\/strong> is: A=14\u03c0r2A = \\frac{1}{4} \\pi r^2<\/p>\n\n\n\n

    Substitute r=1r = 1 cm: A=14\u22c53.1416\u22c5(1)2=3.14164=0.7854\u2009cm2A = \\frac{1}{4} \\cdot 3.1416 \\cdot (1)^2 = \\frac{3.1416}{4} = 0.7854 \\, \\text{cm}^2<\/p>\n\n\n\n

    \n\n\n\n

    Final Answer:<\/strong><\/h3>\n\n\n\n

    0.7854\u2009cm2\\boxed{0.7854 \\, \\text{cm}^2}<\/p>\n\n\n\n

    \n\n\n\n

    Explanation<\/strong><\/h3>\n\n\n\n

    To find the area of a quarter circle with a given perimeter of 3.57 cm, we begin by recalling the formula for the perimeter of a quarter circle. A quarter circle consists of two straight sides (both equal to the radius) and a curved arc, which is one-fourth of the full circle\u2019s circumference. The total perimeter is thus made up of the arc length and the two radii.<\/p>\n\n\n\n

    Mathematically, the perimeter PP of a quarter circle is given by: P=\u03c0r2+2rP = \\frac{\\pi r}{2} + 2r<\/p>\n\n\n\n

    We substitute the known value of the perimeter, 3.57 cm, into this equation and solve for rr, the radius. Using the approximate value of \u03c0\\pi as 3.1416, we get: 1.5708r+2r=3.57\u21d23.5708r=3.571.5708r + 2r = 3.57 \\Rightarrow 3.5708r = 3.57<\/p>\n\n\n\n

    Solving for rr, we find that the radius is approximately 1 cm.<\/p>\n\n\n\n

    Next, we use the formula for the area of a circle: A=\u03c0r2A = \\pi r^2<\/p>\n\n\n\n

    To find the area of a quarter circle, we multiply this by 14\\frac{1}{4}. Substituting r=1r = 1 cm, the area becomes: 14\u22c53.1416\u22c512=0.7854\u2009cm2\\frac{1}{4} \\cdot 3.1416 \\cdot 1^2 = 0.7854 \\, \\text{cm}^2<\/p>\n\n\n\n

    This calculation shows that when the perimeter of a quarter circle is 3.57 cm, the radius is 1 cm, and the area is approximately 0.7854 square centimeters<\/strong>.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    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 given its perimeter, we need to first understand the formula for the perimeter of a quarter circle and use it to find the radius, then use […]<\/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-224831","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224831","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=224831"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224831\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224831"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224831"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224831"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}