{"id":238411,"date":"2025-06-18T05:37:37","date_gmt":"2025-06-18T05:37:37","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=238411"},"modified":"2025-06-18T05:37:39","modified_gmt":"2025-06-18T05:37:39","slug":"find-the-area-of-the-shaded-region-of-each-circle-answer-the-questions-that-follow","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/18\/find-the-area-of-the-shaded-region-of-each-circle-answer-the-questions-that-follow\/","title":{"rendered":"Find the area of the shaded region of each circle Answer the questions that follow."},"content":{"rendered":"\n

Find the area of the shaded region of each circle Answer the questions that follow. 1. A 90\u00b0 3. Q 45\u00b0 135\u00b0 X C 6 cm B S 12 cm R Z 8 cm Y<\/p>\n\n\n\n

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

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

To find the area of the shaded regions in each circle, we use the formula for the area of a sector. The formula is given as<\/p>\n\n\n\n

Area of sector = (\u03b8 \/ 360) \u00d7 \u03c0r\u00b2<\/p>\n\n\n\n

where \u03b8 is the central angle in degrees and r is the radius of the circle.<\/p>\n\n\n\n

For the first circle:<\/p>\n\n\n\n

\u03b8 = 90\u00b0 r = 6 cm<\/p>\n\n\n\n

Area = (90 \/ 360) \u00d7 \u03c0 \u00d7 6\u00b2 = (1\/4) \u00d7 \u03c0 \u00d7 36 = 9\u03c0 cm\u00b2<\/p>\n\n\n\n

For the second circle:<\/p>\n\n\n\n

\u03b8 = 45\u00b0 r = 12 cm<\/p>\n\n\n\n

Area = (45 \/ 360) \u00d7 \u03c0 \u00d7 12\u00b2 = (1\/8) \u00d7 \u03c0 \u00d7 144 = 18\u03c0 cm\u00b2<\/p>\n\n\n\n

For the third circle:<\/p>\n\n\n\n

\u03b8 = 135\u00b0 r = 8 cm<\/p>\n\n\n\n

Area = (135 \/ 360) \u00d7 \u03c0 \u00d7 8\u00b2 = (3\/8) \u00d7 \u03c0 \u00d7 64 = 24\u03c0 cm\u00b2<\/p>\n\n\n\n

Explanation:<\/p>\n\n\n\n

Each shaded region in the image represents a sector of a circle. To find the area of a sector, we determine what fraction of the total circle the sector occupies based on its central angle. Since the total circle has an area of \u03c0r\u00b2, we multiply this by the fraction \u03b8\/360 to get the sector’s area.<\/p>\n\n\n\n

For the first circle, the shaded region is one-fourth of the total circle because the central angle is 90\u00b0. Multiplying one-fourth by the total area \u03c0 \u00d7 36 gives 9\u03c0 cm\u00b2. For the second circle, the shaded region is one-eighth of the total circle because the central angle is 45\u00b0. One-eighth of \u03c0 \u00d7 144 gives 18\u03c0 cm\u00b2. For the third circle, the sector is three-eighths of the circle since 135\u00b0 is three-eighths of 360\u00b0. Multiplying three-eighths by \u03c0 \u00d7 64 yields 24\u03c0 cm\u00b2.<\/p>\n\n\n\n

These calculations illustrate the relationship between angle size and sector area. A larger angle results in a larger fraction of the circle being shaded. This principle is useful in fields like engineering and architecture where circular sectors are commonly used.<\/p>\n\n\n\n

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

Find the area of the shaded region of each circle Answer the questions that follow. 1. A 90\u00b0 3. Q 45\u00b0 135\u00b0 X C 6 cm B S 12 cm R Z 8 cm Y The Correct Answer and Explanation is: To find the area of the shaded regions in each circle, we use the […]<\/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-238411","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238411","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=238411"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238411\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=238411"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=238411"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=238411"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}