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. 10 : 17

2. 20 : 27

3. 17 : 27

4. 20 : 37

Let radius and heights of two cylinders be r₁, h₁ and r₂, h₂.

Given, $\dfrac{h$1}{h2} = \dfrac{5}{3} \text{ and } \dfrac{r1}{r2} = \dfrac{2}{3}.

Volume of cylinder 1 = V₁ and

Volume of cylinder 2 = V₂.

$\dfrac{V$1}{V2} = \dfrac{πr1^2h1}{πr2^2h2} \\[1em] = \Big(\dfrac{r1}{r2}\Big)^2 \times \dfrac{h1}{h2} \\[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 2 is the correct option.