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A spherical balloon has a 16-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?

User Lashon
by
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1 Answer

14 votes
14 votes

Answer:

a. 2144.66 cubic inches

b.1072.33 cubic inches.

c. 16 inches

Explanation:

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

Volume of sphere: 4/3 π r³

Since diameter (d) = 2 radius (r)

Replacing with the value given:

16 =2r

16/2=r

r= 8 in

Back with the volume formula:

V = 4/3 π r³

V =4/3 π (8)³

V = 2144.66 cubic inches

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

2144.66/2 = 1072.33 cubic inches.

To find the radius of the half-inflated balloon we have to apply again the volume formula and substitute v=1072.33

1072.33 = 4/3 π r³

Solving for r

1072.33 / (4/3 π)= r³

256= r³

16 = r

r = 16 inches

User MrO
by
3.1k points