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

Answer:

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

Step-by-step 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

$V=\frac{4}{3}\pi r^{3}$

we have

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

substitute

$V=\frac{4}{3}\pi (3)^{3}$

$V=36\pi\ in^3$

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

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