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

Answer: Option D

Let their radii be R and r
Then,
$$\begin{array}{rl}& \frac{\frac{4}{3}\pi R^3}{\frac{4}{3}\pi r^3}=\frac{64}{27}\\ & \Rightarrow {\left(\frac{R}{r}\right)}^3=\frac{64}{27}\\ & \Rightarrow {\left(\frac{R}{r}\right)}^3={\left(\frac{4}{3}\right)}^3\\ & \Rightarrow \frac{R}{r}=\frac{4}{3}\end{array}$$
Ratio of surface areas :
$$\begin{array}{rl}& =\frac{4\pi R^2}{4\pi r^2}={\left(\frac{R}{r}\right)}^2\\ & ={\left(\frac{4}{3}\right)}^2\\ & =\frac{16}{9}\\ & =16:9\end{array}$$