Which of the following is the circumference of the circle whose area is equal to the area of a square whose perimeter is 49 inches?<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n To find the circumference of the circle whose area is equal to the area of a square with a given perimeter, we need to break down the problem step by step.<\/p>\n\n\n\n We are told that the perimeter of the square is 49 inches. The perimeter ( P ) of a square is calculated as: The area ( A_{\\text{square}} ) of a square is given by: Next, we need to find the radius of a circle whose area is equal to the area of the square. The area ( A_{\\text{circle}} ) of a circle is given by: The circumference ( C ) of a circle is given by the formula: Thus, the circumference of the circle is approximately 43.42 inches<\/strong>.<\/p>\n\n\n\n The circle whose area is equal to the area of the square with a perimeter of 49 inches has a circumference of approximately 43.42 inches<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" Which of the following is the circumference of the circle whose area is equal to the area of a square whose perimeter is 49 inches? The correct answer and explanation is : To find the circumference of the circle whose area is equal to the area of a square with a given perimeter, we need […]<\/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-201375","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/201375","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=201375"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/201375\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=201375"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=201375"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=201375"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Determine the side length of the square.<\/h3>\n\n\n\n
[
P = 4 \\times \\text{side length}
]
Given ( P = 49 ) inches, we can solve for the side length of the square:
[
49 = 4 \\times \\text{side length}
]
[
\\text{side length} = \\frac{49}{4} = 12.25 \\text{ inches}
]<\/p>\n\n\n\nStep 2: Calculate the area of the square.<\/h3>\n\n\n\n
[
A_{\\text{square}} = \\text{side length}^2
]
Substituting the side length we found:
[
A_{\\text{square}} = 12.25^2 = 150.0625 \\text{ square inches}
]<\/p>\n\n\n\nStep 3: Find the radius of the circle with the same area.<\/h3>\n\n\n\n
[
A_{\\text{circle}} = \\pi r^2
]
where ( r ) is the radius of the circle. Since the area of the circle is equal to the area of the square, we set the two areas equal:
[
\\pi r^2 = 150.0625
]
Now, solve for ( r^2 ):
[
r^2 = \\frac{150.0625}{\\pi}
]
[
r^2 = \\frac{150.0625}{3.1416} \\approx 47.75
]
[
r = \\sqrt{47.75} \\approx 6.91 \\text{ inches}
]<\/p>\n\n\n\nStep 4: Calculate the circumference of the circle.<\/h3>\n\n\n\n
[
C = 2\\pi r
]
Substituting the radius we found:
[
C = 2 \\times 3.1416 \\times 6.91 \\approx 43.42 \\text{ inches}
]<\/p>\n\n\n\nConclusion:<\/h3>\n\n\n\n