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


Answer :

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.

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