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If two cones have their heights in the ratio 1:3 and radii 3:1 , then the ratio of their volumes is

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3:1

1:3

1:9

9:1

answer is A.

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Detailed Solution

Cones:

$h_{1} : h_{2} = 1 : 3$

$r_{1} : r_{2} = 3 : 1$

$\frac{v_{1}}{v_{2}} = \frac{\frac{1}{3} π r_{1}^{2} h_{1}}{\frac{1}{3} π r_{2}^{2} h_{1}}$

$= {(\frac{3}{1})}^{2} . \frac{1}{3}$

$= 3 : 1$

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