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

Answer 1

(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$=\frac{\mathrm{\pi }{\left(3r\right)}^2\times \left(2h\right)}{{\displaystyle \frac{1}{3}}\mathrm{\pi }{\left(4r\right)}^2\times \left(3h\right)}$
$$\begin{gathered} =\frac{9r^2\times 2\times 3}{16r^2\times 3} \\ =\frac{9}{8} \\ =9:8 \end{gathered}$$