Saturday, July 16, 2011

Summer Problem Solving Marathon Solution #35

The volume of a sphere is (4/3)π r3, so the volume of the hemisphere of ice cream is (2/3)π 23 = (16/3)π.

The volume of a cone is (1/3)hB, where B is the area of the circular base of the cone. Here the height is 8, and the circular base has radius 2 and hence area 4π. So the volume of the cone is (32/3)π.

Thus the total volume of ice cream is (16/3)π + (32/3)π = (48/3)π = 16π.

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