Answer:
The volume of a single tennis ball is ![14.14\ in^{3}](https://tex.z-dn.net/?f=14.14%5C%20in%5E%7B3%7D)
The volume of three tennis balls is ![42.42\ in^{3}](https://tex.z-dn.net/?f=42.42%5C%20in%5E%7B3%7D)
Step-by-step explanation:
Step 1
Find the volume of a single tennis ball
we know that
The volume of a sphere is equal to
![V=\frac{4}{3}\pi r^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E%7B3%7D)
where r is the radius of the sphere
In this problem
![r=3/2=1.5\ in](https://tex.z-dn.net/?f=r%3D3%2F2%3D1.5%5C%20in)
substitute
![V=\frac{4}{3}\pi (1.5)^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20%281.5%29%5E%7B3%7D)
![V=14.14\ in^{3}](https://tex.z-dn.net/?f=V%3D14.14%5C%20in%5E%7B3%7D)
Step 2
Find the volume of the can
we know that
the volume of the cylinder is equal to
![V=\pi r^{2} h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E%7B2%7D%20h)
where r is the radius of the cylinder
h is the height of the cylinder
in this problem we have
![r=3/2=1.5\ in](https://tex.z-dn.net/?f=r%3D3%2F2%3D1.5%5C%20in)
![h=8.4\ in](https://tex.z-dn.net/?f=h%3D8.4%5C%20in)
substitute
![V=\pi (1.5)^{2}(8.4)](https://tex.z-dn.net/?f=V%3D%5Cpi%20%281.5%29%5E%7B2%7D%288.4%29)
![V=59.38\ in^{3}](https://tex.z-dn.net/?f=V%3D59.38%5C%20in%5E%7B3%7D)
Statement
<u>case A)</u> The volume of a single tennis ball is ![14.14\ in^{3}](https://tex.z-dn.net/?f=14.14%5C%20in%5E%7B3%7D)
The statement is true
See the procedure in Step 1
<u>case B)</u> The volume of the can is ![56.55\ in^{3}](https://tex.z-dn.net/?f=56.55%5C%20in%5E%7B3%7D)
The statement is false
The volume of the can is
--> see the procedure Step 2
<u>case C)</u> The empty space inside the can is ![14.13\ in^{3}](https://tex.z-dn.net/?f=14.13%5C%20in%5E%7B3%7D)
The statement is false
To find the empty space subtract the volume of three tennis ball from the volume of the can
![59.38\ in^{3}-3*14.14\ in^{3}=16.96\ in^{3}](https://tex.z-dn.net/?f=59.38%5C%20in%5E%7B3%7D-3%2A14.14%5C%20in%5E%7B3%7D%3D16.96%5C%20in%5E%7B3%7D)
<u>case D)</u> The volume of three tennis balls is ![42.42\ in^{3}](https://tex.z-dn.net/?f=42.42%5C%20in%5E%7B3%7D)
The statement is true
To find the volume of three tennis balls multiply the volume of a single tennis ball by three
![14.14*3=42.42\ in^{3}](https://tex.z-dn.net/?f=14.14%2A3%3D42.42%5C%20in%5E%7B3%7D)