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Related rates Balloon question. Thanks

  1. Nov 5, 2012 #1
    1. The problem statement, all variables and given/known data

    Air is being pumped into a spherical balloon. Suppose we know the surface area of the balloon increases at a rate of 20cm^2/s when its radius is 4cm. What is the rate its volume is changing at that instant?


    2. Relevant equations



    3. The attempt at a solution

    I went....

    dv/dt = 4∏ (4)^2 * 20/1 = 1280∏

    I know its wrong. Anyone help me out? What am i doing wrong?
     
    Last edited: Nov 5, 2012
  2. jcsd
  3. Nov 5, 2012 #2
    Wait no, I went:

    dv/dt = (1/4pi(4)^2) *20/1

    gives me 5 / 16pi
     
  4. Nov 6, 2012 #3

    haruspex

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    I think that's still wrong. Write out generic formulae for dV/dt and dA/dt as functions of r and dr/dt..
     
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