Two cones have their heights in the ratio 1 : 3 and radii in the ratio 3 : 1. Then ratio of their volume is:

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Solution

Q.
Two cones have their heights in the ratio 1 : 3 and radii in the ratio 3 : 1. Then ratio of their volume is:

1 1 : 3

2 2 : 3

3 3 : 1

4 1 : 1

Ans.
(3)

Let height of the cones are h and 3h respectively and their radii are 3r and r respectively.

∴ Ratio of volumes = $\frac{volume of first cone}{volume of second cone} = \frac{\frac{1}{3} π (3 r)^{2} \times h}{\frac{1}{3} π r^{2} \times 3 h} = \frac{9}{3} = \frac{3}{1} ∴ R e q u i r e d r a t i o i s 3 : 1 .$

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