Math CentralQuandaries & Queries


Question from Libby, a student:

A giant scoop, operated by a crane, is in the shape of a hemisphere of radius 24 inches. The scoop is filled with molten steel. The steel is then poured into a cylindrical storage tank with diameter 32 inches. How high will the molten steel rise?

I got the volume of the hemisphere and the volume of the cylinder, but I'm not exactly sure what to do next.

Hi Libb,

The hemisphere of radius 24 inches is full so the volume is 4/3 π 243 cubic inches. The cylinder has radius 16 inches so is volume is π 162 h cu inches. Thus pi 162 h = 4/3 π 243. Solve for h.


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