How Deep Digging?

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.)


Answer:

The outline of a circle is always 2 * Pi * R (R = the radius). Therefore, the radius will have to
decrease by: 100 centimetres / (2 * Pi) = 100 / 6.28 = R = 15.92 cm. So, to put the cable tightly around the moon the groove should be 15.92 centimetres deep. Which is still a huge task if you want to get this deep all around the moon. The funny thing is that the depth of the groove does not depend on the radius of the object you are digging it in. You could as well 'dig a groove' in the globe on your desk: it would still have to be 15.92 cm.
centimetres.