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

Answer 1

(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.

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