Presumably "unit" cylinders have diameter 2 and height 2 x oo ? I don't believe this. It's obviously true in the limit of infinitely many cylinders with axes distributed uniformly, around a circle or sphere, say. On the other hand, if there's just one cylinder, the ratio is only two! Fred Lunnon On 1/3/11, Dan Asimov <dasimov@earthlink.net> wrote:
Let C_k, k = 1,2,3, . . . , n, . . . be solid unit cylinders in 3-space whose axes all contain the origin.
Let X denote the intersection of all the C_k's.
Prove that the surface area of X is exactly three times its volume.
--Dan
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