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meerkat18

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.

Answer:

Radius of the balloon is 6 in.

Step-by-step 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.

\(Volume\:of\:Sphere=\frac{4}{3}\times\pi r^3\)

\(288\pi=\frac{4}{3}\times\pi r^3\)

\(r^3=\frac{288\times\pi\times3}{4\times\pi}\)

\(r^3=72\times3\)

\(r^3=216\)

\(r=\sqrt[3]{216}\)

\(r=6\)

Therefore, Radius of the balloon is 6 in.

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