Question

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

Answer 1

Let the diameter of earth be d. Therefore, the diameter of moon will be $\frac{d}{4}$.

Radius of the earth $r_e=\frac{d}{2}$
Radius of the moon $r_m=\frac{d}{8}$

We know that surface area of sphere =$4\pi r^2$
∴ The surface area of moon = $4\pi r^2$
The ratio of their surface areas $=\frac{ 4\pi r^2}{4\pi R^2}$
$= \frac{r^2}{R^2}$

$= (\frac{r}{R})^2$

$= (\frac{1}{4})^2$

$=\frac{ 1}{16}$

Therefore, the ratio between their surface areas will be 1:16.