If the ratio of the diameters of the two spheres is 3 : 5, then the ratio of their surface areas is

1. 3 : 5

2. 5 : 3

3. 27 : 125

4. 9 : 25

Let the diameters of two spheres be 3a and 5a.

So, their radius will be $r$1 = \dfrac{3a}{2} \text{ and } r2 = \dfrac{5a}{2}.

$\text{Ratio of their surface area } = \dfrac{4πr$1^2}{4πr2^2} \\[1em] = \dfrac{\Big(\dfrac{3a}{2}\Big)^2}{\Big(\dfrac{5a}{2}\Big)^2} \\[1em] = \dfrac{\Big(\dfrac{9a^2}{4}\Big)}{\Big(\dfrac{25a^2}{4}\Big)} \\[1em] = \dfrac{9a^2 \times 4}{25a^2 \times 4} \\[1em] = \dfrac{9}{25} \\[1em] = 9 : 25.

Hence, Option 4 is the correct option.