Question

Josh finds that his new ball fits tightly inside his cylindrical can of diameter 6 inches and height 5 inches. What is the exact amount of empty space is there inside the can?

Answer 1

The exact amount of empty space is
`9\pi\ in^3`

Explanation:

we know that

To find out the exact amount of empty space, subtract the volume of the ball from the volume of the cylindrical can

step 1

Find the volume of teh ball

The volume of the sphere (ball) is given by

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

we have

`r=6/2=3\ in` ---> the radius is half the diameter

substitute

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

`V=36\pi\ in^3`

step 2

Find the volume of the cylinder

The volume of the cylinder is given by

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

we have

`r=6/2=3\ in` ---> the radius is half the diameter

`h=5\ in`

substitute

`V=\pi (3)^(2) (5)`

`V=45\pi\ in^3`

step 3

Subtract the volumes

`V=45\pi-36\pi=9\pi\ in^3`