Question

The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface areas.

Answer 1

Surface area of sphere $=\pi d^2=4\pi r^2$

Surface area of moon = $\pi d_1^2$

Surface area of earth = $\pi d_2^2$

Given: $\frac{d_1}{d_2}=\frac{1}{4}$

Ratio of surface areas $=\frac{\pi d_1^2}{\pi d_2^2}=(\frac{1}{4}{)}^2$

$=\frac{1}{16}$