In the puzzle statement, "A six inch high cylindrical hole is drilled through the center of a sphere," through is the keyword, rather than into.
I made the same initial mistake of misreading through as into.
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.