Author: Robert Hyatt
Date: 09:14:20 02/10/06
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I only gave this a couple of minutes thought. I'm not 100% certain that the largest displacement would be produced by a sphere _totally_ contained in the cone, although intuition says that is correct. But it would be trivial to handle this. Find the largest circle with center at the center of the base, that still fits inside the cone. Then slowly reduce the radius as the circle center moves up the centerline of the cone, and see if the volume of the part of the sphere inside the cone increases. I'm puzzled by the "order" as IMHO #2 is probably the hardest to do by a significant amount. It isn't what I would call "hard" at all, but it is something that would take some time to actually write and test...
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