Brain teaser--I just don't understand it

This came from “Ask Marilyn.” It was a couple of years ago, so I might be missing some details but here goes:

The upshot, IIRC, is that if you drill a hole thru a ball, the volume of the remaining sphere will be the same, regardless of the diameter of the hole that you just drilled.

That can not possibly be correct, so what am I remembering incorrectly???

Nothing. If you drill a hole through a sphere such that the remaining part has a given length (say an inch), the volume left doesn’t depend on how big of a sphere you started with, as long as the diameter is least that length.

It is too clear, and so it is hard to see.

All of Marilyn’s questions that I have seen so far rely on them being misunderstood to be taken for something obviously wrong. Then someone explains the real question and answer and it looks like they done something miraculous.

For example: The Monty Hall problem.