The radii of the bases of a cylinder and a cone are in the ratio 3 : 4 and their heights are in the ratio 2 : 3.

Question:

The radii of the bases of a cylinder and a cone are in the ratio 3 : 4 and their heights are in the ratio 2 : 3. Then, their volumes are in the ratio
(a) 9 : 8
(b) 8 : 9
(c) 3 : 4
(d) 4 : 3

Solution:

(a)  9 : 8

Suppose that the respective radii of the cylinder and the cone are 3r and 4r and their respective heights are 2h and 3h.

$\therefore$ Ratio of the volumes $=\frac{\pi(3 r)^{2} \times 2 h}{\frac{1}{3} \pi(4 r)^{2} \times 3 h}=\frac{3 \times 9 \times 2}{16 \times 3}=\frac{9}{8}$

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