If the circumferences of two circles are in the ratio 4: 9 then the ratio in their area is

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9: 4

4: 9

2: 3

16: 81

answer is D.

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Detailed Solution

Given that the circumferences of two circles are in the ratio 4: 9.
We have to find the ratio of their areas.
The area of a circle can be expressed as

A = π r 2

, where r is the radius of a circle.
The ratio of the circumferences

C 1 a n d C 2

is,

Therefore, the ratio of their areas,

A 1 a n d Α 2

is,

A 1 A 2 = π r 1 2 π r 2 2 ⇒ A 1 A 2 = 492 ⇒ A 1 A 2 = 1681

Therefore, the ratio of their area is 16:81.
Therefore, the correct option is 4.

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