Question

how much empty space is inside the can of tennis balls? the radius of each tennis ball is 1.5 inches. The radius of the can is 1.75 inches and the height is 9 inches. Use 3.14 for pi, and round your answers to the nearest hundredth.

Answer 1

`44.16\ in^(3)`

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

`V=(4)/(3)\pi r^(3)`

we have

`r=1.5\ in`

substitute

`V=(4)/(3)\pi (1.5)^(3)=4.5 \pi\ in^(3)`

therefore

The volume of three tennis balls is equal to

`(3)4.5 \pi=13.5 \pi\ in^(3)`

step 2

Find the volume of the can

The volume of the cylinder (can) is equal to

`V=\pi r^(2) h`

we have

`r=1.75\ in`

`h=9\ in`

substitute the values

`V=\pi (1.75)^(2) (9)=27.5625 \pi\ in^(3)`

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

`27.5625 \pi\ in^(3)-13.5 \pi\ in^(3)=14.0625 \pi\ in^(3)`

use
`\pi=3.14`

`14.0625(3.14)=44.16\ in^(3)`