{"id":234259,"date":"2025-06-14T03:12:11","date_gmt":"2025-06-14T03:12:11","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=234259"},"modified":"2025-06-14T03:12:13","modified_gmt":"2025-06-14T03:12:13","slug":"find-the-arc-length-indicated-by-the-bolded-arc","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/14\/find-the-arc-length-indicated-by-the-bolded-arc\/","title":{"rendered":"Find the arc length indicated by the bolded arc"},"content":{"rendered":"\n

Find the arc length indicated by the bolded arc 2 mi 0 J) 8.4 mi D \u00e2\u201a\u00ac 60.2 mi D’b) 9.4 mi 0 d 117.8 mi D A 8 Previous<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

Correct Answer: a) 8.4 mi<\/strong><\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

This problem requires us to find the length of a specific arc of a circle. The arc length is the distance along the curved line that makes up the arc.<\/p>\n\n\n\n

1. Identify Given Information:<\/strong>
From the provided image, we can identify two key pieces of information:<\/p>\n\n\n\n

    \n
  • Radius (r):<\/strong>\u00a0The radius of the circle is given as\u00a02 mi<\/strong>.<\/li>\n\n\n\n
  • Central Angle (\u03b8):<\/strong>\u00a0The angle that subtends the bolded arc is given in radians as\u00a04\u03c0\/3<\/strong>.<\/li>\n<\/ul>\n\n\n\n

    2. Select the Appropriate Formula:<\/strong>
    The formula for calculating the arc length (s) of a circle depends on the unit of the central angle. When the central angle (\u03b8) is given in radians, the formula is:<\/p>\n\n\n\n

    s = r * \u03b8<\/p>\n\n\n\n

    Where:<\/p>\n\n\n\n

      \n
    • s\u00a0is the arc length.<\/li>\n\n\n\n
    • r\u00a0is the radius of the circle.<\/li>\n\n\n\n
    • \u03b8\u00a0is the central angle in radians.<\/li>\n<\/ul>\n\n\n\n

      This formula is a direct and efficient way to find the arc length because the definition of a radian is based on the ratio of arc length to the radius.<\/p>\n\n\n\n

      3. Substitute Values and Calculate:<\/strong>
      Now, we substitute the given values into the formula:<\/p>\n\n\n\n

        \n
      • r = 2 mi<\/li>\n\n\n\n
      • \u03b8 = 4\u03c0\/3<\/li>\n<\/ul>\n\n\n\n

        s = 2 * (4\u03c0\/3)
        s = 8\u03c0 \/ 3 mi<\/p>\n\n\n\n

        This is the exact arc length in terms of \u03c0. To find the numerical value that matches the multiple-choice options, we will use the approximation for \u03c0 \u2248 3.14159.<\/p>\n\n\n\n

        s \u2248 (8 * 3.14159) \/ 3
        s \u2248 25.13272 \/ 3
        s \u2248 8.37757 mi<\/p>\n\n\n\n

        4. Compare and Conclude:<\/strong>
        The calculated arc length is approximately 8.37757 mi. We now compare this value to the given options:<\/p>\n\n\n\n

          \n
        • a) 8.4 mi<\/li>\n\n\n\n
        • b) 9.4 mi<\/li>\n\n\n\n
        • c) 60.2 mi<\/li>\n\n\n\n
        • d) 117.8 mi<\/li>\n<\/ul>\n\n\n\n

          Our calculated value, when rounded to one decimal place, is 8.4 mi<\/strong>. This matches option (a).<\/p>\n\n\n\n

          Therefore, the length of the bolded arc is 8.4 mi.thumb_upthumb_down<\/p>\n\n\n\n

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

          Find the arc length indicated by the bolded arc 2 mi 0 J) 8.4 mi D \u00e2\u201a\u00ac 60.2 mi D’b) 9.4 mi 0 d 117.8 mi D A 8 Previous The Correct Answer and Explanation is: Correct Answer: a) 8.4 mi Explanation: This problem requires us to find the length of a specific arc of […]<\/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-234259","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234259","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=234259"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234259\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=234259"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=234259"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=234259"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}