A circle has an area of 64\u03c0 in2. Which of the following is the circumference of the circle in terms of pi ( \u03c0)?<\/p>\n\n\n\n
A.
9 \u03c0 in<\/p>\n\n\n\n
B.
16 \u03c0 in<\/p>\n\n\n\n
C.
4 \u03c0 in<\/p>\n\n\n\n
D.
8 \u03c0 in<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To find the circumference of a circle given its area, we need to follow a series of steps involving the formulas for the area and circumference of a circle. Here\u2019s a detailed explanation:<\/p>\n\n\n\n Step 1: Understand the given information.<\/strong> The area of the circle is given as 64\u03c064\\pi64\u03c0 square inches. We need to find the circumference of the circle in terms of \u03c0\\pi\u03c0.<\/p>\n\n\n\n Step 2: Use the formula for the area of a circle.<\/strong> The formula for the area AAA of a circle is: A=\u03c0r2A = \\pi r^2A=\u03c0r2 where rrr is the radius of the circle.<\/p>\n\n\n\n We are given that: A=64\u03c0A = 64\\piA=64\u03c0<\/p>\n\n\n\n Substitute 64\u03c064\\pi64\u03c0 into the area formula: 64\u03c0=\u03c0r264\\pi = \\pi r^264\u03c0=\u03c0r2<\/p>\n\n\n\n Step 3: Solve for the radius rrr.<\/strong> To isolate r2r^2r2, divide both sides of the equation by \u03c0\\pi\u03c0: 64=r264 = r^264=r2<\/p>\n\n\n\n Now, solve for rrr by taking the square root of both sides: r=64r = \\sqrt{64}r=64\u200b r=8 inchesr = 8 \\text{ inches}r=8 inches<\/p>\n\n\n\n Step 4: Use the formula for the circumference of a circle.<\/strong> The formula for the circumference CCC of a circle is: C=2\u03c0rC = 2\\pi rC=2\u03c0r<\/p>\n\n\n\n Substitute r=8r = 8r=8 inches into the circumference formula: C=2\u03c0\u00d78C = 2\\pi \\times 8C=2\u03c0\u00d78 C=16\u03c0 inchesC = 16\\pi \\text{ inches}C=16\u03c0 inches<\/p>\n\n\n\n Step 5: Review the options.<\/strong> The circumference of the circle is 16\u03c016\\pi16\u03c0 inches, which corresponds to option B.<\/p>\n\n\n\n Conclusion:<\/strong> The correct answer is B. 16\u03c016\\pi16\u03c0 inches.<\/p>\n\n\n\n Explanation Summary:<\/strong> To find the circumference from the area, first, determine the radius using the area formula. Then use the radius in the circumference formula. By calculating, we find the radius is 8 inches and thus the circumference is 16\u03c016\\pi16\u03c0 inches. This step-by-step approach ensures accurate conversion from area to circumference.<\/p>\n","protected":false},"excerpt":{"rendered":" A circle has an area of 64\u03c0 in2. Which of the following is the circumference of the circle in terms of pi ( \u03c0)? A.9 \u03c0 in B.16 \u03c0 in C.4 \u03c0 in D.8 \u03c0 in The Correct Answer and Explanation is: To find the circumference of a circle given its area, we need to […]<\/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-135600","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/135600","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=135600"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/135600\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=135600"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=135600"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=135600"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}