Friday puzzle: sphere

Last week’s puzzle was about a man who went on a triangular walk and shoots a bear. The well-known solution is that the man must be at the North Pole (since the triangle returns him to his starting place) so the bear must be white. Less well known is that the man can be near the South Pole too (yes, I know there are no polar bears in the Antarctic; there are none at the North Pole either, in fact). The key is that when the man walks one mile east in the middle of his walk, he must go all the way around the world, which he can do if he starts a bit more than a mile from the South Pole. In fact, at an infinite number of places since anywhere on that circle of latitude will do. But wait, there’s more. He could also go twice around the world if he was a bit nearer. Or three times. In fact there are an infinite number of rings near the south pole where he could start.

Today’s puzzle keeps on the spherical theme. A hole 6” long is drilled through a sphere. What volume remains?

And a bonus spherical puzzle that is very simple but surprising if you’ve never seen it. A string is stretched around the equator (that’s about 25,000 miles long). Simultaneously, a lot of people lift the string up 3 feet all around the world. How much extra string do you need?