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The radii of two circles are in the ratio $2 : 3$ . The ratio of their areas is,

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2 : 3

4 : 9

9 : 4

8 : 27

answer is B.

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Detailed Solution

It is given that the radii of two circles are in the ratio

2 : 3

. We need to find the ratio of their areas.
Let the radii of two circles be

r

and

R

respectively.
By data,

r : R = 2 : 3

We know that the area of a circle with radius

r

units is

π r^{2}

sq.units.
Therefore,
Area of circle with radius

r

a = π r^{2}

sq.units — (1)
Area of circle with radius

r

A = π R^{2}

sq.units — (2)
From eq(1) and Eq(2),

Ratio of areas = \frac{π r^{2}}{π R^{2}}

\Rightarrow Ratio of areas = (\frac{r}{R})^{2}

\Rightarrow Ratio of areas = (\frac{2}{3})^{2}

\Rightarrow Ratio of areas = \frac{4}{9}

Therefore, when the radii of two circles are in the ratio

2 : 3

, the ratio of their areas is

4 : 9

.
Hence, the correct option is 2.

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