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Q.

The circumference of two circles are in the ratio 4: 25. Find the ratio of their area.


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a

21:81

b

81:21

c

26:81

d

16:625 

answer is D.

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Detailed Solution

Given that the circumference of two circles area in the ratio 4: 25.
We have to find the ratio of their area.
The area of a circle can be expressed as A=π r 2  , where r is the radius of a circle.
Consider C 1  , and C 2   be the circumferences of two circles.
So, the ratio of the circumferences is,
Question ImageTherefore, the ratio of their area is,
A 1 A 2 = π r 1 2 π r 2 2   ⇒ A 1 A 2 = 4 25 2 ⇒ A 1 A 2 = 16 625  
The ratio of their area is 16:625.
Therefore, the correct option is 4.
 
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