Question

If the amount of air in a spherical balloon is 288 pi cu. in.,

what is the radius of the balloon?

Answer 1

Radius of the balloon is 6 in.

Explanation:

Given: Amount of Air in balloon =
`288\pi\,in.^3`

Shape of balloon is sphere .

To find: radius of balloon.

Let r be the radius of sphere or balloon.

We use formula of volume of sphere.

`Volume\:of\:Sphere=(4)/(3)*\pi r^3`

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

`r^3=(288*\pi*3)/(4*\pi)`

`r^3=72*3`

`r^3=216`

`r=\sqrt[3]{216}`

`r=6`

Therefore, Radius of the balloon is 6 in.

Answer 2

The balloon assumes the shape of a sphere with a formula of the volume equal to V = 4/3 pi r^3 where r is the radius of the balloon. In this case, we are given with volume of 288 pi in^3. We just substitute the given volume such that the resulting radius that answers the problem is 6 inches.