Question

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? (6 points) π(10in)2(3in) − 1.5( four over three π(8in)3) π(3in)2(10in) − 1.5( four over three π(8in)3) π(10in)2(3in) − 8( four over three π(1.5in)3) π(3in)2(10in) − 8( four over three π(1.5in)3) I got the answer as the fourth one however im unsure if I am correct.

Answer 1

Answer:

  π(3 in)²(10 in) -8(4/3)(1.5 in)³

Step-by-step explanation:

The volume of a cylinder with a radius of 3 inches and a height of 10 inches is ...

  V = πr²h = π(3 in)²(10 in)

The volume of 8 spheres with a radius of 1.5 inches is ...

  V = 8(4/3)πr³ = 8(4/3)π(1.5 in)³

The volume occupied by the water is the volume of the cylinder not occupied by the spheres. So, it is ...

  V = π(3 in)²(10 in) -8(4/3)(1.5 in)³ . . . . . . matches the 4th choice