Question: A sphere of radius 1 overlaps a smaller sphere of radius r in such a way that their intersection is a circle of radius r.

A sphere of radius 1 overlaps a smaller sphere of radius r in such a way that their intersection is a circle of radius r. (In other words, they intersect in a great circle of the small sphere.) Find r so that the volume inside the small sphere and outside the large sphere is as large as possible.

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