A solid is a cylinder of radius r and height h with a hemisphere of radius r fixed on top. The hemisphere's volume is exactly one-third of the cylinder's volume. Then h equals:

Question

Accepted Answer

2r. Set 2/3\π r^3 = 1/3(\π r^2 h) . Multiply both sides by 3 and cancel \π r^2 : 2r = h , so h = 2r. Choosing r comes from equating the two volumes instead of using the one-third condition; 3r comes from multiplying by 3 on the wrong side; r/2 inverts the relation.

A solid is a cylinder of radius r and height h with a hemisphere of radius r fixed on top. The hemisphere's volume is exactly one-third of the cylinder's volume. Then h equals:

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