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Q.

If the radii of two cones are in the ratio 2:1 and their volumes are equal, then the ratio of their heights is

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a

1:4

b

1:2

c

4:1

d

1:8

answer is B.

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Detailed Solution

Ratio of radii of two cones = 2:1

$\frac{r_{1}}{r_{2}} = \frac{2}{1}$

$v_{1} = v_{2}$

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

$\frac{h_{1}}{h_{2}} = {(\frac{r_{2}}{r_{1}})}^{2}$

$\frac{h_{1}}{h_{2}} = {(\frac{2}{1})}^{2} = \frac{4}{1}$

$h_{1} : h_{2} = 4 : 1$

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If the radii of two cones are in the ratio 2:1 and their volumes are equal, then the ratio of their heights is