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 \(V=288\pi\)
The volume of a sphere is given by
\(V=\frac{4}{3}\pi r^3\)
On substituting the value, we get
\(288\pi=\frac{4}{3}\pi r^3\)
Cancel π from both side
\(288=\frac{4}{3} r^3\)
Solving the equation for r
\(r^3=\frac{288\times3}{4}\\\\r^3=216\\\\r=6\)
Therefore, the radius of the balloon is 6 inches.
