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.)

C = pi * d
C = pi * 1738000 = 5460088.0319390606484480742001398

But your rope is 1m short, so...
C-1 = 5460087.0319390606484480742001398

Then back-figure the new diameter:

d' = C / pi

d' = 1737999.6816901138162093284622325

d - d' = 0.31830988618379067153776752674501m deep

But that's the total depth for two hemispheres, so cut that in half:

r' = 0.1591549430918953357688837633725

David Rowley is correct!

Posted by Tim on 2002-05-07 08:59:17