A spherical balloon has a 34-in. diameter when it is fully inflated. Half of the air is let out of the balloon. Assume that the balloon remains a sphere.

a. Find the volume of the fully-inflated balloon.

b. Find the volume of the half-inflated balloon.

c. What is the radius of the half-inflated balloon?

a. 20,579.52 cubic inches

b. 10,289.76 cubic inches.

c. 13.49 inches

Step-by-step explanation:

Hi, to answer this question we have to calculate the volume of a sphere:

Volume of a sphere: 4/3 π r³

Since diameter (d) = 2 radius (r)

Replacing with the value given:

34 = 2r

34/2=r

r = 17 in

Back with the volume formula:

V = 4/3 π r³

V = 4/3 π (17) ³

V = 20,579.52 cubic inches

The volume of the half-inflated balloon is equal to the volume of the sphere divided by 2.

20,579.52/2 = 10,289.76 cubic inches.

To find the radius of the half-inflated balloon we have to apply again the volume formula and substitute v=10,289.76

10,289.76 = 4/3 π r³

Solving for r

10,289.76 / (4/3 π) = r³

2,456.5 = r³

∛2,456.5 = r

r = 13.49 inches