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The radii of a cylinder and a cone are in the relation 3:4 and their heights are in the ratio 2:3. Then, their volumes are in the ratio ____.

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Detailed Solution

The radii of a cylinder and a cone are in the relation 3:4 and their heights are in the ratio 2:3. Then, their volumes are in the ratio 9:8.
Given, the radii of a cylinder and a cone are in the relation 3:4 and their heights are in the ratio 2:3.
We know that the volume of a cone is

\frac{1}{3} π r^{2} h

and the volume of the cylinder is

π R^{2} H

.
So, the ratio of the volumes is

\frac{π R^{2} H}{\frac{1}{3} π r^{2} h}

.

= 3 (\frac{H}{h}) (\frac{R}{r})^{2}

= 3 (\frac{2}{3}) (\frac{3}{4})^{2}

=

\frac{9}{8}

So, the required ratio is 9:8.
Hence, the correct answer is 9:8.

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