A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 8 marbles, each of diameter 3 inches. The vase is filled with water up to a height of 10 inches.

Which of the following could be used to calculate the volume of water in the vase?

π (10in) 2 (3in) - 1.5 (four over threeπ (8in) 3)

π (3in) 2 (10in) - 1.5 (four over threeπ (8in) 3)

π (10in) 2 (3in) - 8 (four over threeπ (1.5in) 3)

π (3in) 2 (10in) - 8 (four over threeπ (1.5in) 3)

The answer is: π (3in) 2 (10in) - 8 (four over threeπ (1.5in) 3)

The volume of water in the vase (V) is a difference between the volume of the cylindrical vase and 8 volumes of the marble:

V = V1 - 8V2

The volume of the cylinder (cylindrical vase) is

V1 = π r1² h,

where:

V1 - the volume of the cylindrical vase,

r1 - the radius of the cylindrical vase,

h - the height of the cylindrical vase.

r1 = 6in : 2 = 3 in

h = 10 in

⇒ V1 = π (3 in) ² · 10 in

The volume of the sphere (marble) is

V2 = 4/3 π r2³

where

V2 - the volume of the marble,

r2 - the radius of the marble.

r2 = 3 in : 2 = 1.5 in

⇒ V2 = 4/3 π (1.5 in) ³

Therefore:

V = V1 - 8V2

V = π (3 in) ² · 10 in - 8 · 4/3 π (1.5 in) ³