{"id":234254,"date":"2025-06-14T03:08:11","date_gmt":"2025-06-14T03:08:11","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=234254"},"modified":"2025-06-14T03:08:13","modified_gmt":"2025-06-14T03:08:13","slug":"find-the-length-of-the-bolded-arc","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/14\/find-the-length-of-the-bolded-arc\/","title":{"rendered":"Find the length of the bolded arc."},"content":{"rendered":"\n

Find the length of the bolded arc. Round your answer to the nearest tenth. 210\u00b0 19 mi<\/p>\n\n\n\n

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

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

Of course. Here is the solution presented in a clear, step-by-step format.<\/p>\n\n\n\n

Finding the Length of a Circular Arc<\/strong><\/h3>\n\n\n\n

Objective:<\/strong>
To find the length of the bolded arc of a circle with a given radius and central angle. The final answer must be rounded to the nearest tenth.<\/p>\n\n\n\n

Underlying Principle:<\/strong>
The length of a circular arc is a fraction of the total circumference of the circle. This fraction is determined by the ratio of the arc’s central angle to the total degrees in a full circle (360\u00b0). The formula for calculating the length of an arc (L) is:<\/p>\n\n\n\n

L = (\u03b8 \/ 360\u00b0) * 2\u03c0r<\/p>\n\n\n\n

where:<\/p>\n\n\n\n

    \n
  • \u03b8<\/strong>\u00a0(theta) is the central angle of the arc in degrees.<\/li>\n\n\n\n
  • r<\/strong>\u00a0is the radius of the circle.<\/li>\n\n\n\n
  • \u03c0<\/strong>\u00a0(pi) is a mathematical constant, approximately equal to 3.14159.<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    Step-by-Step Solution:<\/strong><\/h3>\n\n\n\n

    1. Identify the Given Information:<\/strong>
    From the provided image, we extract the necessary values:<\/p>\n\n\n\n

      \n
    • The central angle,\u00a0\u03b8 = 210\u00b0<\/strong>.<\/li>\n\n\n\n
    • The radius of the circle,\u00a0r = 19 mi<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      2. Substitute the Values into the Formula:<\/strong>
      We will now substitute the identified values for \u03b8 and r into the arc length formula:<\/p>\n\n\n\n

      L = (210 \/ 360) * 2 * \u03c0 * 19<\/p>\n\n\n\n

      3. Perform the Calculation:<\/strong>
      First, we can simplify the fraction and the expression:<\/p>\n\n\n\n

      L = (210\/360) * 38\u03c0<\/p>\n\n\n\n

      The fraction 210\/360 simplifies to 21\/36, which further simplifies to 7\/12.<\/p>\n\n\n\n

      L = (7\/12) * 38\u03c0
      L = (266\/12)\u03c0
      L \u2248 22.166… * \u03c0<\/p>\n\n\n\n

      Now, we multiply by the value of \u03c0 (\u2248 3.14159):<\/p>\n\n\n\n

      L \u2248 22.166… * 3.14159
      L \u2248 69.63864… mi<\/p>\n\n\n\n

      4. Round to the Nearest Tenth:<\/strong>
      The problem asks us to round the final answer to the nearest tenth.<\/p>\n\n\n\n

        \n
      • The calculated length is 69.63864…<\/li>\n\n\n\n
      • The digit in the tenths place is\u00a06<\/strong>.<\/li>\n\n\n\n
      • The digit immediately to its right (in the hundredths place) is\u00a03<\/strong>.<\/li>\n<\/ul>\n\n\n\n

        Since 3 is less than 5, we keep the tenths digit as it is and drop the remaining decimal places.<\/p>\n\n\n\n

        Final Answer:<\/strong>
        The length of the bolded arc is 69.6 mi<\/strong>.thumb_upthumb_down<\/p>\n\n\n\n

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

        Find the length of the bolded arc. Round your answer to the nearest tenth. 210\u00b0 19 mi The Correct Answer and Explanation is: Of course. Here is the solution presented in a clear, step-by-step format. Finding the Length of a Circular Arc Objective:To find the length of the bolded arc of a circle with 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-234254","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234254","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=234254"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234254\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=234254"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=234254"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=234254"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}