Answer:
[tex]44.16\ in^{3}[/tex]
Step-by-step explanation:
I assume that there are 3 tennis balls inside the can
step 1
Find the volume of each tennis ball
we know that
The volume of the sphere (tennis ball) is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=1.5\ in[/tex]
substitute
[tex]V=\frac{4}{3}\pi (1.5)^{3}=4.5 \pi\ in^{3}[/tex]
therefore
The volume of three tennis balls is equal to
[tex](3)4.5 \pi=13.5 \pi\ in^{3}[/tex]
step 2
Find the volume of the can
The volume of the cylinder (can) is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=1.75\ in[/tex]
[tex]h=9\ in[/tex]
substitute the values
[tex]V=\pi (1.75)^{2} (9)=27.5625 \pi\ in^{3}[/tex]
step 3
To find the empty space inside the can subtract the volume of the three tennis ball from the volume of the can
so
[tex]27.5625 \pi\ in^{3}-13.5 \pi\ in^{3}=14.0625 \pi\ in^{3}[/tex]
use [tex]\pi=3.14[/tex]
[tex]14.0625(3.14)=44.16\ in^{3}[/tex]
