Question

the circumference of two circle are in the ratio 2:3 . find the ratios of their areas

Answer 1

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ratio of circumference=2:3

ratio of radius=circumference/circumference=2πr/2πr

2/3=2πr/2πr

r/r=2/3=2:3

ratio of area=πr square/πr square

( pie and square will be cancelled)

=4/9

=4:9

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Answer 2

$\frac{2\pi \: r1}{2\pi \: r2} = \frac{2}{3} \\ = > r1 = \frac{2}{3} \times r2 - - - - - - - 1$
From eq. 1,
$\frac{\pi {r1}^{2} }{\pi {r2}^{2} } \\ = \frac{ { (\frac{2}{3} r2)}^{2} }{ {r2}^{2} } \\ = \frac{4}{9}.$




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