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A sphere of radius 1 overlaps a smaller sphere of radius r in such a way that

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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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A typical sphere of radius r is shown in the figure We wish to maximize the shaded v...View the full answer


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