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.)

It doesn't look like the actual circumference matters. The grove will be the difference between the original and the final radius.

C=2*pi*r therefore r = C/(2*pi)

original r - new r
= C/(2*pi) - (C-1)/(2*pi)
= (C-(C-1))/2*pi
=1/(2*pi)

Looks good to me, anyways.
I keep thinking I'm missing something but the math seems right.

Posted by John on 2002-05-07 12:28:11