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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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