{"id":234245,"date":"2025-06-14T02:52:30","date_gmt":"2025-06-14T02:52:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=234245"},"modified":"2025-06-14T02:52:32","modified_gmt":"2025-06-14T02:52:32","slug":"for-questions-13-and-14-find-the-length-13-232-5-mm","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/14\/for-questions-13-and-14-find-the-length-13-232-5-mm\/","title":{"rendered":"For questions 13 and 14, find the length 13. 232\u00b0 5 mm"},"content":{"rendered":"\n

For questions 13 and 14, find the length 13. 232\u00b0 5 mm<\/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 detailed, textbook-style explanation.<\/p>\n\n\n\n

Solution for Question 13: Finding the Length of an Arc<\/strong><\/h3>\n\n\n\n

Objective:<\/strong> To calculate the length of the major arc of a circle with a given radius and central angle.<\/p>\n\n\n\n

Introduction:<\/strong>
An arc is a portion of the circumference of a circle. The length of an arc is determined by the size of its central angle and the radius of the circle. The problem provides a circle with a radius of 5 mm and indicates a major arc defined by a central angle of 232\u00b0. The task is to find the length of this specific arc.<\/p>\n\n\n\n

Principle and Formula:<\/strong>
The length of an arc is a fraction of the total circumference of the circle. This fraction is equal to the ratio of the arc’s central angle (\u03b8) to the total angle in a circle (360\u00b0).<\/p>\n\n\n\n

The formula for the circumference of a circle is:<\/p>\n\n\n\n

    \n
  • C = 2\u03c0r<\/li>\n<\/ul>\n\n\n\n

    Combining these, the formula for the length of an arc (L) is:<\/p>\n\n\n\n

      \n
    • L = (\u03b8 \/ 360\u00b0) \u00d7 2\u03c0r<\/li>\n<\/ul>\n\n\n\n

      Step-by-Step Calculation:<\/strong><\/p>\n\n\n\n

        \n
      1. Identify the given values:<\/strong>\n
          \n
        • Radius (r) = 5 mm<\/li>\n\n\n\n
        • Central Angle (\u03b8) = 232\u00b0<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • Substitute the values into the arc length formula:<\/strong>\n
            \n
          • L = (232 \/ 360) \u00d7 2\u03c0(5)<\/li>\n<\/ul>\n<\/li>\n\n\n\n
          • Simplify the expression:<\/strong>\n
              \n
            • First, calculate the full circumference: C = 2\u03c0(5) = 10\u03c0 mm.<\/li>\n\n\n\n
            • The formula becomes: L = (232 \/ 360) \u00d7 10\u03c0<\/li>\n<\/ul>\n<\/li>\n\n\n\n
            • Reduce the fraction (232\/360):<\/strong>\n
                \n
              • To simplify the calculation, the fraction can be reduced by finding a common divisor. Both 232 and 360 are divisible by 8.<\/li>\n\n\n\n
              • 232 \u00f7 8 = 29<\/li>\n\n\n\n
              • 360 \u00f7 8 = 45<\/li>\n\n\n\n
              • The simplified fraction is 29\/45.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
              • Calculate the exact arc length:<\/strong>\n
                  \n
                • Substitute the reduced fraction back into the equation: L = (29\/45) \u00d7 10\u03c0<\/li>\n\n\n\n
                • Multiply the terms: L = (290\u03c0 \/ 45)<\/li>\n\n\n\n
                • Simplify this final fraction by dividing the numerator and denominator by 5:<\/li>\n\n\n\n
                • L = (58\u03c0 \/ 9) mm<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n

                  This result, (58\u03c0\/9) mm<\/strong>, is the exact length of the arc.<\/p>\n\n\n\n

                    \n
                  1. Calculate the approximate decimal value:<\/strong>\n
                      \n
                    • For a numerical approximation, use \u03c0 \u2248 3.14159.<\/li>\n\n\n\n
                    • L \u2248 (58 \/ 9) \u00d7 3.14159<\/li>\n\n\n\n
                    • L \u2248 6.444… \u00d7 3.14159<\/li>\n\n\n\n
                    • L \u2248 20.246 mm<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n

                      Final Answer:<\/strong>
                      The length of the arc subtended by the 232\u00b0 angle is exactly (58\u03c0\/9) mm<\/strong>. Rounding to two decimal places, the approximate length is 20.25 mm<\/strong>.thumb_upthumb_down<\/p>\n\n\n\n

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

                      For questions 13 and 14, find the length 13. 232\u00b0 5 mm The Correct Answer and Explanation is: Of course. Here is the solution presented in a detailed, textbook-style explanation. Solution for Question 13: Finding the Length of an Arc Objective: To calculate the length of the major arc of a circle with a given radius […]<\/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-234245","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234245","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=234245"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234245\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=234245"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=234245"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=234245"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}