Answer:
The volume of the area not occupied by the tennis balls is 12.28 cubic inches.
Step-by-step explanation:
It is given that tennis balls with a diameter of 2.5in are sold in cans of three. the can is a cylinder.
Radius of ball = Radius of can = [tex]\frac{2.5}{2}=1.25[/tex]
Height of can = [tex]2.5\times 3=7.5[/tex]
The volume of sphere is
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
where, r is radius of sphere.
The volume of a tennis balls is
[tex]V=\dfrac{4}{3}\pi (1.25)^3[/tex]
[tex]V=8.18123[/tex]
[tex]V\approx 8.18[/tex]
Volume of three tennis balls is
[tex]V_1=3\times 8.18=24.54[/tex]
The volume of cylinder is
[tex]V=\pi r^2h[/tex]
The volume of can is
[tex]V_2=\pi (1.25)^2(7.5)[/tex]
[tex]V_2=36.81553[/tex]
[tex]V_2\approx 36.82[/tex]
The volume of the area not occupied by the tennis balls is
Volume = Volume of cylinder - Volume of three tennis balls
= 36.82 - 24.54 = 12.28 inches
Therefore, the volume of the area not occupied by the tennis balls is 12.28 cubic inches.
