What I mean is if you drill 6 inches into the earth, you haven't passed through the other side...
edit: I think they mean drill a 6 inch hole of maximum width, which of course would just leave a very thin ring of the earth 6 inches tall.
It also doesn't even state that the hole must enter the sphere. A large solid sphere that internally contains a six inch hole through its center would qualify too.
This was my objection when I first encountered the problem. Everyone else seemed to understand that the hole must pass through both sides of the sphere, but that's not stated or even implied in the problem.
I made the same initial mistake of misreading through as into.
With a sufficiently wide hole, you could indeed drill a 6" hole through a spherical Earth, it'd just look more like a thin ring the diameter of the Earth than a sphere.
i think it would be more clear to phrase it starting along the lines of: position a cylinder concentric and inscribed within a sphere ...
I guess the overall idea is anyway to reveal the elegant mathematical result. Wikipedia does a good job of talking clearly about it:
In geometry, the volume of a band of specified height around a sphere—the part that remains after a hole in the shape of a circular cylinder is drilled through the sphere—does not depend on the sphere's radius.