Imagine you would have to put a rope around the moon. Since the moon is 1,738,000 metres in diameter, this is a hard task. Finally you have managed to get the rope around the moon but... it is one meter short.

You decide to dig a groove all around the moon, so that the shorter rope suffices. How deep must this groove be? (Assume the Moon to be a perfect sphere.)

Your current circumferrence (C1) - whatever is is, is 1 meter too long for you. So you need to create a second one - C2 - which would be one meter less.

C1 - 1 = C2

Now let's express that in terms of their respective radii - R1 and R2:

2(pi)R1 - 1 = 2(pi)R2
2(pi)(R1 - R2) = 1
(R1 - R2) = 1/(2*pi)

Remember - we are looking for the depth of the groove wich is the difference between R1 and R2, and it will remain constant even as the radii change.

Posted by levik on 2002-05-08 11:34:48