A circle has an area of 49\u03c0 in2. Which of the following is the circumference of the circle in terms of pi (\u03c0)?<\/p>\n\n\n\n
A.
14 \u03c0 in<\/p>\n\n\n\n
B.
28 \u03c0 in<\/p>\n\n\n\n
C.
7 \u03c0 in<\/p>\n\n\n\n
D.
3.5 \u03c0 in<\/p>\n\n\n\n
The Correct answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To solve this problem, we need to determine the circumference of the circle given its area. The key to solving this lies in understanding the relationship between the area, radius, and circumference of a circle.<\/p>\n\n\n\n The area AAA of a circle is given by the formula:A=\u03c0r2A = \\pi r^2A=\u03c0r2<\/p>\n\n\n\n where rrr is the radius of the circle.<\/p>\n\n\n\n We know the area of the circle is 49\u03c049\\pi49\u03c0 square inches:49\u03c0=\u03c0r249\\pi = \\pi r^249\u03c0=\u03c0r2<\/p>\n\n\n\n To find the radius rrr, divide both sides by \u03c0\\pi\u03c0:r2=49r^2 = 49r2=49<\/p>\n\n\n\n Taking the square root of both sides gives:r=49=7 inchesr = \\sqrt{49} = 7 \\text{ inches}r=49\u200b=7 inches<\/p>\n\n\n\n The circumference CCC of a circle is given by the formula:C=2\u03c0rC = 2\\pi rC=2\u03c0r<\/p>\n\n\n\n Substitute the radius r=7r = 7r=7 inches into the formula:C=2\u03c0(7)=14\u03c0 inchesC = 2\\pi(7) = 14\\pi \\text{ inches}C=2\u03c0(7)=14\u03c0 inches<\/p>\n\n\n\n The correct answer is A. 14\u03c0 in<\/strong>.<\/p>\n\n\n\n The area of the circle was provided as 49\u03c049\\pi49\u03c0 square inches. Using the area formula A=\u03c0r2A = \\pi r^2A=\u03c0r2, we found the radius rrr to be 7 inches. With this radius, we applied the circumference formula C=2\u03c0rC = 2\\pi rC=2\u03c0r and calculated the circumference to be 14\u03c014\\pi14\u03c0 inches. The key steps involved recognizing how to extract the radius from the area and then applying it to the circumference formula. Understanding these fundamental formulas allows us to transition between area, radius, and circumference, highlighting their interconnectedness.<\/p>\n","protected":false},"excerpt":{"rendered":" A circle has an area of 49\u03c0 in2. Which of the following is the circumference of the circle in terms of pi (\u03c0)? A.14 \u03c0 in B.28 \u03c0 in C.7 \u03c0 in D.3.5 \u03c0 in The Correct answer and Explanation is: To solve this problem, we need to determine the circumference of the circle given […]<\/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-133950","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/133950","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=133950"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/133950\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=133950"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=133950"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=133950"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Use the formula for the area of a circle.<\/h3>\n\n\n\n
Step 2: Plug in the given area.<\/h3>\n\n\n\n
Step 3: Solve for the radius.<\/h3>\n\n\n\n
Step 4: Use the formula for the circumference of a circle.<\/h3>\n\n\n\n
Conclusion:<\/h3>\n\n\n\n
Explanation:<\/h3>\n\n\n\n