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Math Help - [SOLVED] rate problem

  1. #1
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    [SOLVED] rate problem

    A spherical balloon is being inflated at a constant rate of 25cm/sec. At what rate in cm/sec is the radius of the balloon changing when the radius is 2cm?

    I have the volume which is 4/3*(pi)*8.

    I thought the answer would be 25 divided by the volume, but I guess I was wrong because the answer key says 25/16pi?

    How would I go about setting this problem up? thanks
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  2. #2
    Eater of Worlds
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    They give you dV/dt=25 and r=2.

    We need dr/dt when r=2

    Differentiate the sphere volume formula:

    4{\pi}r^{2}\frac{dr}{dt}=25

    Now, plug in r=2 and solve for dr/dt
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