I don't know hers, but here's mine. I first saw this problem in my
freshman physics course. You can still use it as a geometry problem if you
tell the students that they don't need to know the radius of the sphere to
solve this problem, or that the problem has an answer with the information
given.
If that's true, then the answer must be the same no matter what the radius
of the sphere is, or the problem would be insolvable, and we are told that
it *is* solvable. So take the radius of the sphere to be 3 inches. Then
the hole is infinitesimally thin, and so the volume outside the hole is
just the volume of the sphere, which is (4/3)*pi*3^3=3D36 pi.
I have no explanation why the excluded volume should be the same for all
such holes, other than to do it by calculus. It's possible that this might
motivate them to learn calculus...;<)
mark snyder
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