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Spherical Balloon - Related Rates Problem

  1. Mar 26, 2008 #1
    [SOLVED] Spherical Balloon - Related Rates Problem

    1. The problem statement, all variables and given/known data
    A spherical balloon is inflated so that its radius increases at a rate of 1 cm/min. How fast is the volume increasing when:

    a) the diameter is 2000 cm
    b) the surface area is 324 pi cm^2 ---> I have solved this already

    2. Relevant equations
    V = (4/3)pi(r^3)
    dV/dt = 4pi(r^2)(dr/dt)

    3. The attempt at a solution

    For part (a) the diameter is 2000 cm.
    So I make it 1000 cm for Radius

    Now, I put it in the equation:

    dV/dt = 4pi(r^2)(dr/dt)

    where dr/dt = 1cm/min

    dV/dt = 4pi(1000^2)(1 cm/min)
    = 4 000 000 pi cm^3 / min

    But, the answer in the book is 40 000 pi cm^3 / min.

    Please help me out. Thanks.
  2. jcsd
  3. Mar 26, 2008 #2


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    Science Advisor
    Homework Helper

    Hi rum2563! :smile:

    Your answer looks right to me.

    I think the book must have meant 200cm, not 2000. :frown:
  4. Mar 26, 2008 #3
    thanks very much. I thought so too. 2000 seems too much exaggerated. I am going to check with my teacher just to make sure. Thanks.
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