{"id":259265,"date":"2025-07-18T20:19:22","date_gmt":"2025-07-18T20:19:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=259265"},"modified":"2025-07-18T20:20:54","modified_gmt":"2025-07-18T20:20:54","slug":"the-diameter-of-a-circle-is-8-inches-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/18\/the-diameter-of-a-circle-is-8-inches-2\/","title":{"rendered":"The diameter of a circle is 8 inches."},"content":{"rendered":"\n<p>The diameter of a circle is 8 inches. What is the angle measure of an arc bounding a sector with an area of 2r square inches? K = \u00ce\u00b8r sq. in d = 8 in Give the exact answer in simplest form. Submit<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-539.png\" alt=\"\" class=\"wp-image-259277\"\/><\/figure>\n\n\n\n<p><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>To solve this problem, we will use the formula for the area of a sector of a circle, which is:A=\u03b8360\u2218\u00d7\u03c0r2A = \\frac{\\theta}{360^\\circ} \\times \\pi r^2A=360\u2218\u03b8\u200b\u00d7\u03c0r2<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>AAA is the area of the sector,<\/li>\n\n\n\n<li>\u03b8\\theta\u03b8 is the central angle of the sector (in degrees),<\/li>\n\n\n\n<li>rrr is the radius of the circle.<\/li>\n<\/ul>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The diameter of the circle is 8 inches, so the radius r=82=4r = \\frac{8}{2} = 4r=28\u200b=4 inches.<\/li>\n\n\n\n<li>The area of the sector is given as 2r2r2r, which is 2\u00d74=82 \\times 4 = 82\u00d74=8 square inches.<\/li>\n<\/ul>\n\n\n\n<p>We are asked to find the angle \u03b8\\theta\u03b8 corresponding to this area. So, substituting into the sector area formula:8=\u03b8360\u2218\u00d7\u03c0(4)28 = \\frac{\\theta}{360^\\circ} \\times \\pi (4)^28=360\u2218\u03b8\u200b\u00d7\u03c0(4)2<\/p>\n\n\n\n<p>Simplifying the equation:8=\u03b8360\u2218\u00d7\u03c0\u00d7168 = \\frac{\\theta}{360^\\circ} \\times \\pi \\times 168=360\u2218\u03b8\u200b\u00d7\u03c0\u00d7168=16\u03c0\u03b8360\u22188 = \\frac{16\\pi\\theta}{360^\\circ}8=360\u221816\u03c0\u03b8\u200b8\u00d7360\u2218=16\u03c0\u03b88 \\times 360^\\circ = 16\\pi\\theta8\u00d7360\u2218=16\u03c0\u03b82880\u2218=16\u03c0\u03b82880^\\circ = 16\\pi\\theta2880\u2218=16\u03c0\u03b8<\/p>\n\n\n\n<p>Now, solving for \u03b8\\theta\u03b8:\u03b8=2880\u221816\u03c0\\theta = \\frac{2880^\\circ}{16\\pi}\u03b8=16\u03c02880\u2218\u200b<\/p>\n\n\n\n<p>Simplify:\u03b8=180\u03c0\u2009degrees\\theta = \\frac{180}{\\pi} \\, \\text{degrees}\u03b8=\u03c0180\u200bdegrees<\/p>\n\n\n\n<p>So, the angle \u03b8\\theta\u03b8 is 180\u03c0\\frac{180}{\\pi}\u03c0180\u200b degrees.<\/p>\n\n\n\n<p>This is the exact answer in its simplest form. To express it as a decimal, 180\u03c0\u224857.3\u2218\\frac{180}{\\pi} \\approx 57.3^\\circ\u03c0180\u200b\u224857.3\u2218, but the exact value is preferred when possible.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-926.jpeg\" alt=\"\" class=\"wp-image-259273\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The diameter of a circle is 8 inches. What is the angle measure of an arc bounding a sector with an area of 2r square inches? K = \u00ce\u00b8r sq. in d = 8 in Give the exact answer in simplest form. Submit The Correct Answer and Explanation is: To solve this problem, we will [&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 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-259265","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259265","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=259265"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259265\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=259265"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=259265"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=259265"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}