Question

The volume of a small rubber ball is 20 cubic inches. If

the radius of the ball were doubled, what would be the
volume of the new, larger ball?

Answer 1

Volume: 160 cubic inches

Explanation:

The formula of a sphere is V =
`(4)/(3)\pi r^3` where r is the radius and V is volume

You can insert 20 as the volume and use it as a way to view the changes:

20 =
`(4)/(3)\pi r^3`

15 =
`\pi r^3`

`(15)/(\pi )` =
`r^3`

now if the radius were doubled...

? =
`(2r)^3`

? = 8
`r^3`

`(15)/(8\pi )` =
`r^3`

Then if you were to compare it to the original volume, you should see that when substituted, it appears as:

? =
`(4)/(3)\pi 8 r^3`

20 * 8 =
`(4)/(3)\pi 8 r^3`

Therefore, the volume of the new, larger ball is 160 cubic inches

Hope that helps : )