Question

A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 9 marbles, each of diameter 2 inches. The vase is filled with water up to a height of 12 inches. What is the volume of water in the vase?

Answer 1

The volume of water in the vase is the difference of volume of cylinder and that of the marbles. 
            Vcylinder = πr²h = π(6 in)²(12 in) = 432π in³
            Vmarbles = 9(4πr³/3) = 9(4π(3 in)³/3) = 324 π in³
The difference of the volumes is 108π in³.