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.)

I did not read the solution and read only the last comment, so I do hope this is not redundant. However, if we allow the moon's diameter to go to zero, we are left with a circle of rope 1 meter circumference or 39.37 inches which when divided by pi gives 12.53186022 inches as the diameter. So, it seems the groove should be half that deep or 6.26593011 inches.

If you think metric, that's 15.91549431 centimeters.

Posted by CeeAnne on 2004-10-27 15:28:24