Question

A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 7 marbles, each of diameter 3 inches. The vase is filled with water up to a height of 12 inches. Which of the following could be used to calculate the volume of water in the vase?

π(12in)2(3in) − 7(four over threeπ(1.5in)3)
π(3in)2(12in) − 7(four over threeπ(1.5in)3)
π(12in)2(3in) − 1.5(four over threeπ(7in)3)
π(3in)2(12in) − 1.5(four over threeπ(7in)3)

Answer 1

second choice

Explanation:

the volume of water in the vase

= volume of the vase up to the height 12 inches - volume of 7 marbles

= π(6/2)²(12) - 7(4/3)π(3/2)³

so answer is the second choice

Answer 2

Explanation:

Vase:

h = 12 in

r = diameter/2 = 6/2 = 3 in

Volume of vase = πr²h

= π(3)²*12

Marbles:

r = 3/2 = 1.5 in

`Volume \ of \ marbles = (4)/(3)\pi r^(3)\\\\\\Volume \ of \ 7 marbles=7*(4)/(3)\pi (1.5)^(3)`

Volume of water = Volume of vase - volume of 7 marbles

`= \pi (3)^(2)*12 - 7*(4)/(3)\pi (1.5)^(3)`