The ratio of area of two circles whose ratio of circumference is 3: 1 will be

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3: 1

1: 3

1: 9

9: 1

answer is D.

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Detailed Solution

Given that, ratio of circumference is 3: 1.
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,
2πm: 2πn = 3: 1
Cancel out

2 π

from left side of the equation.
m: n = 3 : 1
Using the area of circle

π r 2

to determine the area,

π m 2 : π n 2 = m 2 : n 2

⇒ 32 : 12

\Rightarrow

9 : 1
Therefore, ratio which represents the area of both circles is 9 : 1 .
Hence the correct option is 4.

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