On Fri, 25 Jan 2002, Tim May wrote:
> I said the height of the _remaining_ portion of the sphere, with the
> core drilled out as described, is 10 cm:
>
> "Appendix: A math puzzle. Imagine a solid sphere. Maybe the sphere is
> made of plutonium. A drill bit is lowered onto the sphere, going right
> through the center, centered on the center (that is, the drilled-out
> core is not off-center in any way. What is left is a sphere with a
> cylindrical section (and the two end caps) removed. The height of the
> remaining part of the sphere is 10 centimeters. What is its volume?"
>
> That rules out "if the drill is wider than the sphere."
Actually it isn't a math problem so much as a word game problem. Since you
postulate a drill of zero size it follows there can't be anything drilled
out and therefore cant' be any 'remaining part'. In fact, one could argue
that since you draw a clear distinction between pre- and post- drilling
(ie remaining) that this in fact excludes a drill of diameter 0.
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