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A sphere is placed inside a right circular cylinder so as to touch the top, base and the lateral surface of the cylinder. If the radius of the sphere is R, the volume of the cylinder is ?
 

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Assuming this is a question you need help with, I think I have an answer:

The cylinder's height is 2R, since the "diameter" of the sphere spans the bottom and top of the cylinder. The radius of the base of the cylinder is just R since the cylinder entirely surrounds the sphere. So, the volume of the cylinder is V=(pi)(R^2)(2R), or 2(pi)R^3.

I'm not sure if that made sense, so please ask more questions if you have any. (I might also be completely wrong, in which case somebody can correct me.)

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