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The circumference of two circles are in the ratio 2:3. The ratio of their areas is

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4: 9

None of these

2: 3

9: 4

answer is B.

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Detailed Solution

Given that, ratio of circumferences of two circles is

2 : 3

.
Consider m and n represents the radius of both circles.
Using the circumference of a circle

2 π r

to determine the value of m and n,

2 π m : 2 π n = 2 : 3

Canceling out from left side of the equation,

m : n = 2 : 3

Using the area of circle

π r 2

to determine the area,

π m 2 : π n 2 = m 2 : n 2

⇒ 22 : 32

⇒

4 : 9
Therefore, ratio which represents the area of both circles is

4 : 9

.
Hence the correct option is 2.

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