Question

A student is trying to calculate the density of a ball. She already knows the mass, but she needs to determine the volume as well. Which of the following formulas can be used to calculate the volume of the ball?

1. V= 4/3 πr^3
2. V=1/3 πr^2h
3. s^3
4. πr^2h

Answer 1

The cone has a height of 10 and a diameter of 6. This means it has a radius of 3.

The volume of any cone is (1/3)πr2h. Therefore the volume of this cone would be (1/3)π(3)2(10) or 30π units3.

The hemisphere has a diameter of 6. This means it also has a radius of 3.

The volume of any sphere is (4/3)πr3. A hemisphere would be half that or (2/3)πr3. Therefore the volume of this hemisphere is (4/3)π(3)3 or 36π units3.The total volume would be 30π + 36π or 66π units3. The decimal approximation is 207.35 units3.

Step-by-step explanation:

Cone: V = (1/3)πr2H

V = (1/3)π(3)2(10)

V = (1/3)π(90)

V = 30π

Hemisphere: V = (1/2)(4/3)πr3

V = (2/3)π(6)3

V = (2/3)π(216)

V = 144π

Total Volume = 30π + 144π = 174π

V ≈ 546.64 units3