{"id":235828,"date":"2025-06-15T19:44:38","date_gmt":"2025-06-15T19:44:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=235828"},"modified":"2025-06-15T19:44:40","modified_gmt":"2025-06-15T19:44:40","slug":"12-m-find-the-area-of-the-shaded-sector-74-7-75-64-25-85-64-92-99","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/15\/12-m-find-the-area-of-the-shaded-sector-74-7-75-64-25-85-64-92-99\/","title":{"rendered":"12 m Find the area of the shaded sector. 74\u00b0 7.75 64.25 85.64 92.99"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">12 m Find the area of the shaded sector. 74\u00b0 7.75 64.25 85.64 92.99<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To find the area of a shaded sector of a circle, the following formula is used:Area&nbsp;of&nbsp;Sector=(\u03b8360)\u00d7\u03c0r2\\text{Area of Sector} = \\left( \\frac{\\theta}{360} \\right) \\times \\pi r^2Area&nbsp;of&nbsp;Sector=(360\u03b8\u200b)\u00d7\u03c0r2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u03b8\\theta\u03b8 is the central angle in degrees<\/li>\n\n\n\n<li>rrr is the radius of the circle<\/li>\n\n\n\n<li>\u03c0\u22483.1416\\pi \\approx 3.1416\u03c0\u22483.1416<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Radius r=12r = 12r=12 meters<\/li>\n\n\n\n<li>Central angle \u03b8=74\u2218\\theta = 74^\\circ\u03b8=74\u2218<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">First, calculate the full area of the circle:\u03c0r2=3.1416\u00d7122=3.1416\u00d7144=452.3904&nbsp;m2\\pi r^2 = 3.1416 \\times 12^2 = 3.1416 \\times 144 = 452.3904 \\text{ m}^2\u03c0r2=3.1416\u00d7122=3.1416\u00d7144=452.3904&nbsp;m2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now calculate the sector&#8217;s area:(74360)\u00d7452.3904=0.20556\u00d7452.3904\u224892.99&nbsp;m2\\left( \\frac{74}{360} \\right) \\times 452.3904 = 0.20556 \\times 452.3904 \\approx 92.99 \\text{ m}^2(36074\u200b)\u00d7452.3904=0.20556\u00d7452.3904\u224892.99&nbsp;m2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the correct answer is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>92.99 m\u00b2<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Explanation (300 words):<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A sector in a circle is a region bounded by two radii and the arc between them. The area of a sector represents a fraction of the area of the full circle, determined by the central angle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The calculation begins with the full circle&#8217;s area, obtained by squaring the radius and multiplying by pi. For a circle with a radius of 12 meters, squaring gives 144. Multiplying 144 by 3.1416 provides the complete area of 452.3904 square meters.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Since the sector only covers part of the circle, the fraction of the circle it represents must be determined. This is done by dividing the given angle, 74\u00b0, by the full circle&#8217;s 360\u00b0. The result is approximately 0.20556. This value is then multiplied by the total area of the circle to find the area specific to the sector.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The product yields approximately 92.99 square meters. This value represents the shaded region enclosed by the two radii forming the 74\u00b0 angle and the arc they intercept. The key to accurate calculation lies in the proper application of the sector formula and careful multiplication.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">From the options provided\u2014<strong>7.75<\/strong>, <strong>64.25<\/strong>, <strong>85.64<\/strong>, and <strong>92.99<\/strong>\u2014only <strong>92.99<\/strong> is consistent with the expected outcome based on the mathematical process.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-665.jpeg\" alt=\"\" class=\"wp-image-235829\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>12 m Find the area of the shaded sector. 74\u00b0 7.75 64.25 85.64 92.99 The Correct Answer and Explanation is: To find the area of a shaded sector of a circle, the following formula is used:Area&nbsp;of&nbsp;Sector=(\u03b8360)\u00d7\u03c0r2\\text{Area of Sector} = \\left( \\frac{\\theta}{360} \\right) \\times \\pi r^2Area&nbsp;of&nbsp;Sector=(360\u03b8\u200b)\u00d7\u03c0r2 Where: Given: First, calculate the full area of the circle:\u03c0r2=3.1416\u00d7122=3.1416\u00d7144=452.3904&nbsp;m2\\pi [&hellip;]<\/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 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