jmc

Question

A hemispherical cup of radius 3 inches is filled with milk. The milk is then poured into a right cylindrical container of radius 2 inches. What is the minimum number of inches in the height of the container so it can hold all of the milk? Express your answer as a decimal to the nearest tenth.

Accepted Answer

The hemisphere-shaped milk cup has volume 12 43 (3^3) = 2 3^2 = 18 cubic inches. A cylindrical container with height h has volume (2^2)(h)=4 h cubic inches. The milk will fit if 4 h 18. Dividing both sides of the inequality by 4 gives h 4.5, so the minimum height is 4.5 inches.