Question

Roger Federer bought a can of three tennis balls as a gift for his nephew. The can is just large enough for the balls to fit inside.

a. What is the volume of the can? Round your answer to the nearest thousandth.


b. What is the volume of the empty space inside the can? Think!


Round your answer to the nearest hundredth.

Incase you can't see the image it is a can with three tennis balls and the can is a diameter of 2.7 inches at the top.

Answer 1

a. 46.35 in ^ 3

b. 15.45 in ^ 3

Explanation:

a. To calculate the volume of a cylinder the formula is as follows:

Vc = pi * (r ^ 2) * h

we know the radius because we know the diameter

r = d / 2

diameter is equal to 2.7, therefore the radius is:

r = 2.7 / 2 = 1.35

on the other hand, the height is the diameter of the balls 3 times, since there are 3 of them:

h = 2.7 * 3 = 8.1

replacing, we are left with:

Vc = 3.14 * (1.35 ^ 2) * 8.1 = 46.35 in ^ 3

b. in this case we must calculate the volume of the 3 tennis balls and subtract it from the volume of the can

A sphere has a volume formula:

Vs = 4/3 * pi * r ^ 3

We already know the radius, so we replace:

Vs = 4/3 * 3.14 * 1.35 ^ 3

Vs = 10.30

But how are 3 balls:

10.30 * 3 = 30.90 in ^ 3

we subtract from the can volume:

46.35 - 30.90 = 15.45 in ^ 3 is the area of the empty region