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

Let the diameter of earth be d.
Therefore, the diameter of moon will be \(\frac{d}{4}\).
Thus, Radius of earth = \(\frac{d}{2}\)
So, Radius of moon = \(\frac{1}{2}\) × \(\frac{d}{4}\) = \(\frac{d}{8}\)
Hence, Surface area of moon = \(4{\pi}(\frac{d}{8})^2\)
And Surface area of earth = \(\frac{4{\pi}(\frac{d}{8})^2}{4{\pi}(\frac{d}{2})^2}\)
So, Required ratio = \(\frac{4}{64} = \frac{1}{16}\)

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