If the ratio of circumference of two circles is $4 : 9$ , then what is the ratio of their areas is?

9 : 4

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16 : 81

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4 : 9

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2 : 3

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Solution

The correct option is C $16 : 81$
Given that $C_{1} : C_{2} = 4 : 9 \Rightarrow 2 π r_{1} : 2 π r_{2} = 4 : 9 \Rightarrow r_{1} : r_{2} = 4 : 9$
We have
$\frac{A_{1}}{A_{2}} = \frac{π r_{1}^{2}}{π r_{2}^{2}} = \frac{4^{2}}{9^{2}} = \frac{16}{81}$
$∴ A_{1}; A_{2} = 16 : 81$

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4 : 9

4 : 9

The circumferences of two circles are in the ratio 3 : 4. The ratio of their area is

(a) 3 : 4 (b) 4 : 3 (c) 9 : 16 (d) 16 : 9

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