If the radii of two spheres are in the ratio 1 : 4, then their surface areas are in the ratio :

Answer: Option D

Let the radii of the two spheres be r and 4r respectively.
Then,
Required ratio :
$$\begin{array}{rl}& =\frac{4\pi r^2}{4\pi {\left(4r\right)}^2}\\ & =\frac{r^2}{16r^2}\\ & =\frac{1}{16}\\ & =1:16\end{array}$$