Question

Question 7
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 the earth be 'd'. Therefore, the diameter of moon will be $\frac{d}{4}$.

Radius of the earth = $\frac{d}{2}$

Radius of the moon = $\frac{1}{2}\times \frac{d}{4}=\frac{d}{8}$

The surface area of sphere = $4\pi r^2$

Surface area of the moon
$=4\pi {\left(\frac{d}{8}\right)}^2$

Surface area of the earth
$=4\pi {\left(\frac{d}{2}\right)}^2$

Required ratio
$=\frac{4}{64}=\frac{1}{16}$

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