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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Parker 2 weeks 2021-10-03T22:19:45+00:00 1 Answer 0

Answers ( )

    0
    2021-10-03T22:21:27+00:00

    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

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