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

Diameter of moon$=\frac{1}{4}$ of diameter of earth
Let radius of earth = r km
then radius of moon $=\frac{1}{4}$ r km
Now surface area of earth $=4\pi r^2$
and surface area of moon $=4\pi {\left(\frac{1}{4}r\right)}^2=4\pi \times \frac{1}{16}{r}^2=\frac{1}{4}\pi r^2$
Now ratio between surface area of moon and earth $=\frac{1}{4}\pi r^2:4\pi r^2=\frac{1}{4}:4=1:16$