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MODELING WITH MATHEMATICS Three tennis balls are stored in a cylindrical container with a height of 8 inches and a radius of 1.43 inches. The circumference of a tennis ball is 8 inches. Round your answers to the nearest hundredth.
I just need help with part b
A picture shows three tennis balls placed one above another in a cylindrical container.

a. Find the volume of a tennis ball. Round your answer to the nearest hundredth.
The volume of a tennis ball is about
cubic inches.
Answer is about 8.65
b. Find the amount of space within the cylinder not taken up by the tennis balls. Round your answer to the nearest hundredth.
The volume of the space within the cylinder not taken up by the tennis balls is about
cubic inches.

Sagot :

The volume of a tennis ball is about 8.65 cubic inches

The volume of the space within the cylinder not taken up by the tennis balls is about 25.44 cubic inches

Calculating volume

From the question, we are to determine the volume of a tennis ball

From the given information,

The circumference of a tennis ball is 8 inches

That is,

C = 2πr (C is circumference)

8 = 2πr

∴ r = 8/2π

r = 4/π inches

This the radius of a tennis ball

Now, for the volume of a tennis ball

Using the formula for calculating the volume of a sphere

[tex]V = \frac{4}{3}\pi r^{3}[/tex]

Then, the volume of a tennis is

[tex]V = \frac{4}{3}\pi \times (\frac{4}{\pi})^{3}[/tex]

[tex]V = \frac{4}{3}\pi \times \frac{64}{\pi^{3}}[/tex]

[tex]V = \frac{256}{3\pi^{2}}[/tex]

V = 8.64607 cubic inches

V ≅ 8.65 cubic inches

Hence, the volume of a tennis ball is about 8.65 cubic inches

b. To find the amount of space within the cylinder not taken up by the tennis balls

First, we will calculate the volume of the cylinder

Using the formula for calculating the volume of a cylinder

V = πr²h

Where V is the volume

r is the radius

and h is the height

From the given information,

r = 1.43 inches

h = 8 inches

Putting the parameters into the formula, we get

V = π × 1.43² × 8

V = 16.3592π

V = 51.39 cubic inches

This is the volume of the cylinder

Now, for the amount of space within the cylinder not taken up by the tennis balls

Since there are three tennis balls,

The amount of space not taken up will be

51.39 cubic inches - 3(8.65 cubic inches)

51.39 cubic inches - 25.95 cubic inches

= 25.44 cubic inches

Hence, the volume of the space within the cylinder not taken up by the tennis balls is about 25.44 cubic inches

Learn more on Calculating volume here: https://brainly.com/question/15217144

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