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Question:

A cylinder whose height is 8 inches has a volume of 128πcm^{3} . If its radius is doubled and its height is cut in half, the volume of the resulting cylinder is

A
256πcm^{3}.

Explaination

The volume of a cylinder is πr^{2}h. In the original cylinder, πr^{2}h = 128π so r^{2}(128π/8π) = 16 and the radius, r, equals √16 = 4. In the new cylinder, the radius is doubled to 8 and the height is cut in half to 4. The resulting volume is π× 8^{2}× 4 = 256π cm^{3}.