The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is

1. 3 : 4

2. 4 : 3

3. 9 : 16

4. 16 : 9

Let the radius of two spheres be r₁ and r₂.

Given ratio of volumes = 64 : 27.

$\Rightarrow \dfrac{\dfrac{4}{3}πr$1^3}{\dfrac{4}{3}πr2^3} = \dfrac{64}{27} \\[1em] \Rightarrow \dfrac{r1^3}{r2^3} = \dfrac{4^3}{3^3} \\[1em] \Rightarrow \Big(\dfrac{r1}{r2}\Big)^3 = \Big(\dfrac{4}{3}\Big)^3 \\[1em] \Rightarrow \dfrac{r1}{r2} = \dfrac{4}{3}.

Ratio of surface areas = $\dfrac{4πr$1^2}{4πr2^2}

$= \dfrac{r$1^2}{r2^2} \\[1em] = \Big(\dfrac{r1}{r2}\Big)^2 \\[1em] = \Big(\dfrac{4}{3}\Big)^2 \\[1em] = \dfrac{16}{9} = 16 : 9.

Hence, Option 4 is the correct option.