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The groove around the moon (Posted on 2002-05-06) Difficulty: 3 of 5
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.)

See The Solution Submitted by charl    
Rating: 2.9167 (12 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution | Comment 11 of 32 |
groove depth of 1/(2*pi) meters ~ 0.159 meters

Current circumference = 1738000*pi, which means the rope is 1738000*pi-1. This will be the new circumference as well. The new diameter will be 1738000 - 2 * g (g = groove depth, x2 because one on each side). So new circumference = (1738000 - 2g)*pi. So 1738000*pi - 1 = (1738000 - 2g)*pi. Work this down, I get a groove depth of 1/(2*pi)
  Posted by Stuff N. Things on 2002-05-07 17:55:53
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