If the perimeter of a circle is equal to that of a square, then the ratio of their areas is
(A) 22 : 7
(B) 14 : 11
(C) 7 : 22
(D) 11: 14
Last updated at Aug. 19, 2021 by Teachoo
Transcript
Question 7 If the perimeter of a circle is equal to that of a square, then the ratio of their areas is (A) 22 : 7 (B) 14 : 11 (C) 7 : 22 (D) 11: 14 Let Radius of circle = r Side of square = a Now, given that Circumference of Circle = Perimeter of Square 2๐r = 4a ๐r = 2a 2a = ๐r a = ๐ /๐ ๐ Now, we need to find ratio between Area of square and circle Circle Area of circle = ๐ ๐^๐ Square Area of square = a2 = (๐/2 ๐)^2 = ๐ ^๐/๐ ๐^๐ Now, (๐จ๐๐๐ ๐๐ ๐๐๐๐๐๐)/(๐จ๐๐๐ ๐๐ ๐๐๐๐๐๐)=(๐๐^๐)/((๐^๐ ๐^๐)/๐) =๐๐^2 ร4/(๐^2 ๐^2 ) =4/(๐ ) =4/(22/7) =(4 ร 7)/22 =(2 ร 7)/11 =๐๐/๐๐ โด Required ratio is 14 : 11 So, the correct answer is (B)
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