Amly has a sphere whose radius is 21 cm. She melts this sphere and prepares a cylinder whose radius is the same as that of the sphere. What is the height of the cylinder?

Since the sphere is melted and recast into a cylinder, their volumes are equal according to the volume conservation principle. The volume of the sphere is four thirds times pi times 21 cubed, and the volume of the cylinder is pi times 21 squared times height. Equating the two gives height equals four thirds times 21, so the height of the cylinder is 28 cm.

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