A cylindrical vase has a diameter of 4 inches. At the bottom of the vase, there are 6 marbles, each of diameter 3 inches. The vase is filled with water up to a height of 8 inches. Which of the following could be used to calculate the volume of water in the vase?

Given:

Cylindrical vase with a diameter of 4 inches.

found at the bottom of the vase, 6 marbles with a diameter of 3 inches each.

Let us find the volume of each shape.

cylindrical vase: V = π r² h

V = π (2in) ² * 8 in

V = π * 4in² * 8 in

V = π * 32 in³

marble: V = 4/3 π r³

V = 4/3 π (1.5in) ³

V = 4/3 π 3.375 in³

V = π * 4.5 in³

(π * 4.5 in³) * 6 marbles = π * 27 in³

Volume of the water = Volume of the vase - Volume of the marbles

V H2O = π * 31 in³ - π * 27 in³

V H2O = π (31 in³ - 27 in³)

V H2O = π * 4 in³

Volume of the water = [π (2in) ² * 8 in] - 6[ 4/3 * π * (1.5in) ³]