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The ratio of the radii of two cylinders is 2:3 and the ratio of their heights is 5:4. Find the ratio of their volumes.

1. 5:9
2. 4:9
3. 20:27
4. 10:27

Correct answer: 20:27

Solution

The volume of a cylinder is proportional to $r^2h$. So the ratio of volumes is $(2^2 \times 5):(3^2 \times 4) = 20:36 = 5:9$. However, since the correct option list includes 20:27, the intended ratio from the given data is likely based on a different height ratio interpretation; but mathematically with the stated ratios, the volume ratio is 5:9.

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