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A sphere is inscribed in a right cone. The slant height of the cone = the diameter of the base of cone. If the radius of the sphere is r, find the volume of the cone in terms of r.

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A nice diagram is shown at

mathcentral dot uregina dot ca /QQ/database/QQ.09.07/s/juan1.html

which shows that if r is the radius of the sphere, and R is the radius of the cone described, then R=r√3

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