{"id":224835,"date":"2025-06-03T14:07:52","date_gmt":"2025-06-03T14:07:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224835"},"modified":"2025-06-03T14:07:55","modified_gmt":"2025-06-03T14:07:55","slug":"the-perimeter-of-a-quarter-circle-is-3-57-kilometers-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/the-perimeter-of-a-quarter-circle-is-3-57-kilometers-2\/","title":{"rendered":"The perimeter of a quarter circle is 3.57 kilometers."},"content":{"rendered":"\n

The perimeter of a quarter circle is 3.57 kilometers. What is the quarter circle’s radius? Use 3.14 for
. P = 3.57 km<\/p>\n\n\n\n

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

To find the radius<\/strong> of a quarter circle<\/strong> with a perimeter of 3.57 kilometers<\/strong>, and using \u03c0 = 3.14, let’s first understand what the perimeter of a quarter circle includes.<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udd35 Formula for the Perimeter of a Quarter Circle:<\/h3>\n\n\n\n

A quarter circle<\/strong> is one-fourth of a full circle. Its perimeter<\/strong> includes:<\/p>\n\n\n\n

    \n
  • One quarter<\/strong> of the circumference<\/strong> of the circle (curved part),<\/li>\n\n\n\n
  • And two straight sides<\/strong> (radius lines).<\/li>\n<\/ul>\n\n\n\n

    So, the formula is: Perimeter=14(2\u03c0r)+2r\\text{Perimeter} = \\frac{1}{4}(2\\pi r) + 2r<\/p>\n\n\n\n

    Simplifying: Perimeter=12\u03c0r+2r\\text{Perimeter} = \\frac{1}{2} \\pi r + 2r<\/p>\n\n\n\n

    Given:<\/p>\n\n\n\n

      \n
    • Perimeter = 3.57 km<\/li>\n\n\n\n
    • \u03c0 = 3.14<\/li>\n<\/ul>\n\n\n\n

      Substitute into the formula: 3.57=12\u22c53.14\u22c5r+2r3.57 = \\frac{1}{2} \\cdot 3.14 \\cdot r + 2r 3.57=1.57r+2r3.57 = 1.57r + 2r 3.57=3.57r3.57 = 3.57r<\/p>\n\n\n\n

      Now, solve for r<\/strong>: r=3.573.57=1r = \\frac{3.57}{3.57} = 1<\/p>\n\n\n\n

      \n\n\n\n

      \u2705 Final Answer:<\/h3>\n\n\n\n

      1 kilometer\\boxed{1 \\text{ kilometer}}<\/p>\n\n\n\n

      \n\n\n\n

      \ud83d\udd0d Explanation<\/h3>\n\n\n\n

      To determine the radius of a quarter circle when given the perimeter, it\u2019s crucial to understand how the shape is constructed. A quarter circle is a sector of a full circle, cut into four equal parts. Its perimeter includes two parts: the curved arc and the two straight radii that meet at the center.<\/p>\n\n\n\n

      The arc length is one-fourth of the total circumference of the full circle. The circumference of a circle is calculated using the formula 2\u03c0r2\\pi r, where rr is the radius and \u03c0\\pi (pi) is approximately 3.14. Since we’re dealing with a quarter of the circle, the arc length is 14\u00d72\u03c0r=12\u03c0r\\frac{1}{4} \\times 2\\pi r = \\frac{1}{2} \\pi r. In addition to the arc, the perimeter includes two straight lines that are both radii of the circle, which add up to 2r2r.<\/p>\n\n\n\n

      So, the total perimeter of the quarter circle is: 12\u03c0r+2r\\frac{1}{2} \\pi r + 2r<\/p>\n\n\n\n

      We are told the perimeter is 3.57 kilometers and \u03c0 is 3.14. Plugging these values into the formula gives: 3.57=1.57r+2r=3.57r3.57 = 1.57r + 2r = 3.57r<\/p>\n\n\n\n

      Solving for rr, we divide both sides by 3.57, giving us r=1r = 1.<\/p>\n\n\n\n

      Thus, the radius of the quarter circle is 1 kilometer<\/strong>.<\/p>\n\n\n\n

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

      The perimeter of a quarter circle is 3.57 kilometers. What is the quarter circle’s radius? Use 3.14 for. P = 3.57 km The Correct Answer and Explanation is: To find the radius of a quarter circle with a perimeter of 3.57 kilometers, and using \u03c0 = 3.14, let’s first understand what the perimeter of a […]<\/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-224835","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224835","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=224835"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224835\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224835"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224835"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224835"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}