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.