Let us compare the relief of two spheres: a billiard ball (radius = 1.125\") and

Question

Let us compare the relief of two spheres: a billiard ball (radius = 1.125") and the Earth (mean radius = 6,371 km). If we were able to examine the billiard ball very closely, we could observe irregularities (which you could think of as topographical bumps and depressions) of up to 0.0025 of an inch (the allowable tolerance according to the Billiard Congress of America). Given that Mount Everest, the highest mountain on Earth, has an elevation of 8,848 meters and the Marianas Trench is 11.04 km below sea level, which sphere has greater relief relative to its radius? As always, show your calculations. For the relief of the billiard ball multiply 0.0025 inches by two (to get ups and downs).

Explanation / Answer

In case of the billiard ball, the total irregularity= 2*0.0025=0.0050"

Therefore, relief=0.005/1.125=0.00442

In case of eart, total irregularity=8.848+11.04=19.888 km

So, relief=19.88/6371=0.00312

So the billiard bal has larger relief than the earth. You can say the earth is rounder than the billiard ball!

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