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Question

A bottled water company has designed a new cup for its dispenser. The cup will be a right circular cone with a three-inch radius. How tall will the cup need to be to hold 93 cubic inches of water? Express your answer to the nearest whole number.

Accepted Answer

The volume of a cone with radius r and height h is 13 r^2 h. Therefore, we want h to satisfy 13 3^2 h 93, or h 933 9.87. Therefore, the height must be 10 inches.