[dotrob]

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.

[delluminatus]

In that case, the statement from the article "We could have a sphere as large as a planet, bore a hole 6" in length through it..." seems inconsistent. Either the cylinder is not 6" long, or it does not go through the sphere.

[maxerickson]

The problem can be rephrased to avoid the ambiguity. Something like "A hole is bored through a sphere such that the void in the remaining material has the shape of a cylinder 6 inches tall".

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.

http://en.wikipedia.org/wiki/Napkin_ring_problem

[galvan]

I thought that at first, but the length of the hole is dependent on the width of the hole. The wider the hole, the shorter, because wider holes remove bigger caps.

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.

[theophrastus]

i still get a confused language impression from that. for me it's the combination of "drill" and "through" (probably was forced to take too much 'wood shop')

i think it would be more clear to phrase it starting along the lines of: position a cylinder concentric and inscribed within a sphere ...