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If the circumference of a circle is equal to the perimeter of a square what is the ratio of the area of the circle to the area of the square?

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22: 7

14: 11

11: 7

4: 1

answer is B.

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Detailed Solution

The circumference of the circle = 2πr
The perimeter of the square = 4a
Hence, 2πr = 4a
Dividing bath side with 2
2r  4a

⇒ 2 2
 2a
⇒ 
Dividing both side with ‘a’
 2a 1
  

a  a
   2
a 
Now, =

area of circle   r2 area of circle a2
 r 2
  
 
r  2

Now substitute a 
 2 2
  
⇒  
 22 
  
 

4
⇒ 

22
Now Taking π as 7

4
22

⇒ 7

47
⇒ 22
28  14
⇒ 22 11
∴ the ratio of the area of circle to the area of square = 14: 11

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