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
Solution:
(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 $=\frac{\pi \times(2 \mathrm{r})^{2} \times 5 h}{\pi \times(3 r)^{2} \times 3 h}$
$=\frac{4 r^{2} \times 5}{9 r^{2} \times 3}$
$=\frac{20}{27}$
$=20: 27$