Question

The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their volumes is
(a) 27 : 20
(b) 20 : 27
(c) 4 : 9
(d) 9 : 4

Answer 1

(b) 20 : 27
Let the radii of the two cylinders be 2r and 3r and their heights be 5h and 3h, respectively.

Then, ratio of their volumes$=\frac{\mathrm{\pi }\times {\left(2\mathrm{r}\right)}^2\times 5h}{\mathrm{\pi }\times {\left(3r\right)}^2\times 3h}$
$$\begin{gathered} =\frac{4r^2\times 5}{9r^2\times 3} \\ =\frac{20}{27} \\ =20:27 \end{gathered}$$