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 :

1. 4 : 9

2. 9 : 4

3. 20 : 27

4. 27 : 20

Let radius and heights of two cylinders be r, h and R, H.

Given,

$\dfrac{\text{r}}{\text{R}} = \dfrac{2}{3} \text{ and } \dfrac{\text{h}}{\text{H}} = \dfrac{5}{3}$

Volume of cylinder 1 = v

Volume of cylinder 2 = V

$\Rightarrow \dfrac{\text{v}}{\text{V}} = \dfrac{π\text{r}^2\text{h}}{π\text{R}^2\text{H}} \\[1em] = \dfrac{\text{r}^2}{\text{R}^2} \times \dfrac{\text{h}}{\text{H}} \\[1em] = \Big(\dfrac{\text{r}}{\text{R}}\Big)^2 \times \dfrac{\text{h}}{\text{H}} \\[1em] = \Big(\dfrac{2}{3}\Big)^2 \times \dfrac{5}{3} \\[1em] = \dfrac{4}{9} \times \dfrac{5}{3} \\[1em] = \dfrac{20}{27}.$

Hence, option 3 is the correct option.