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

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  1. Chapter 12 Class 10 Areas related to Circles (Term 1)
  2. Serial order wise

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 2๐œ‹r = 4a ๐œ‹r = 2a 2a = ๐œ‹r a = ๐…/๐Ÿ ๐’“ Now, we need to find ratio between Area of square and circle Circle Area of circle = ๐…๐’“^๐Ÿ Square Area of square = a2 = (๐œ‹/2 ๐‘Ÿ)^2 = ๐…^๐Ÿ/๐Ÿ’ ๐’“^๐Ÿ Now, (๐‘จ๐’“๐’†๐’‚ ๐’๐’‡ ๐’„๐’Š๐’“๐’„๐’๐’†)/(๐‘จ๐’“๐’†๐’‚ ๐’๐’‡ ๐’”๐’’๐’–๐’‚๐’“๐’†)=(๐œ‹๐’“^๐Ÿ)/((๐œ‹^๐Ÿ ๐’“^๐Ÿ)/๐Ÿ’) =๐œ‹๐‘Ÿ^2 ร—4/(๐œ‹^2 ๐‘Ÿ^2 ) =4/(๐œ‹ ) =4/(22/7) =(4 ร— 7)/22 =(2 ร— 7)/11 =๐Ÿ๐Ÿ’/๐Ÿ๐Ÿ โˆด Required ratio is 14 : 11 So, the correct answer is (B)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.