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 know this is an old problem but nobody seems to have seen the elegant calculus solution which clearly shows what's happening!
For any circle, C = 2 (pi) R
Differentiate: dC = 2(pi) dR which gives the change in C
In this case, dC = 1, so dR = 1/(2*pi) = 0.159 meters or 15.9 cm
Counter-intuitively, the circumference, isn't needed!
Voila. :-)
A different (and simple) approach
