Question

Tennis balls with a diameter of 2.5 inches are sold in cans of three. The can is a cylinder. What is the volume of the space NOT occupied by the tennis balls? (Assume the tennis balls touch the can on all sides, top and bottom.) Round to the nearest tenth and show all steps and reasoning.

Answer 1

The space NOT occupied by the tennis balls is 12.26 cube inches.

Explanation:

The space NOT occupied = volume of cylinder - total volume of spheres

The can is cylinder with volume =
`\pi`
`r^(2)`h

where r is the radius and h the height of the cylinder

With the given condition,

r =
`(diameter)/(2)` =
`(2.5)/(2)`

= 1.25 inches

h = 3 x diameter = 3 x 2.5

= 7.5 inches

So that,

Volume of the can =
`(22)/(7)` x
`(1.25)^(2)` x 7.5

= 36.830

Volume of can is 36.83 cube inches.

The tennis ball is a sphere with volume =
`(4)/(3)`
`\pi`
`r^(3)`

=
`(4)/(3)` x
`(22)/(7)` x
`(1.25)^(3)`

= 8.185

Volume of the tennis ball is 8.19 cube inches.

Since they are sold in three's, then;

total volume of the tennis balls = 3 x 8.19

= 24.57

Volume of the tennis balls is 24.57 cube inches.

Thus,

The space NOT occupied = 36.83 - 24.57

= 12.26

The space NOT occupied by the tennis balls is 12.26 cube inches.