## 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 rema

Question

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?

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2021-10-03T22:19:45+00:00
2021-10-03T22:19:45+00:00 1 Answer
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## Answers ( )

Answer: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