Question:
The radii of the base of a cylinder and a cone are in the ratio 3 : 4. If their heights are in the ratio 2 : 3, the ratio between their volumes is
(a) 9 : 8
(b) 3 : 4
(c) 8 : 9
(d) 4 : 3
Solution:
(a) 9 : 8
Let the radii of the base of the cylinder and cone be 3r and 4r and their heights be 2h and 3h, respectively.
Then, ratio of their volumes $=\frac{\pi(3 r)^{2} \times(2 h)}{\frac{1}{3} \pi(4 r)^{2} \times(3 h)}$
$=\frac{9 r^{2} \times 2 \times 3}{16 r^{2} \times 3}$
$=\frac{9}{8}$
$=9: 8$
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