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Q.

The radii of two cylinders are in the ratio of 2:5 and their heights are in the ratio of

7:3. Then, the ratio of their volumes is ____.

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Detailed Solution

The radii of two cylinders are in the ratio of 2:5 and their heights are in the ratio of
7:3. Then, the ratio of their volumes is 28:75.
Given, the radii of two cylinders are in the ratio 2:5 and their heights are in the ratio 7:3.
Let the radii be r and R and the heights be h and H.

\frac{r}{R} = \frac{2}{5}

and

\frac{h}{H} = \frac{7}{3}

We know that the volume of a cylinder is

π r^{2} h

.
So the ratio of their volumes=

\frac{π r^{2} h}{π R^{2} H}

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

= \frac{7}{3} (\frac{2}{5})^{2}

= \frac{28}{75}

So the required ratio is 28:75.
Hence, the correct answer is 28:75.

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