Answer:
Radius of the balloon is 6 inches.
Step-by-step explanation:
We have been given that amount of air in a spherical balloon is 288π cu in.
It means the volume of the spherical balloon is [tex]V=288\pi[/tex]
The volume of a sphere is given by
[tex]V=\frac{4}{3}\pi r^3[/tex]
On substituting the value, we get
[tex]288\pi=\frac{4}{3}\pi r^3[/tex]
Cancel π from both side
[tex]288=\frac{4}{3} r^3[/tex]
Solving the equation for r
[tex]r^3=\frac{288\times3}{4}\\\\r^3=216\\\\r=6[/tex]
Therefore, the radius of the balloon is 6 inches.
