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Math Help - Related Rates (implicit differentiation)

  1. #1
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    Related Rates (implicit differentiation)

    Air is being pumped into a spherical balloon so that its volume increases at a rate of 80cm^3/s . How fast is the surface area of the balloon increasing when its radius is 11cm ?

    ... i found the derivative of Surface Area to be 8*pi*r*(dv/dt)=(ds/dt)

    i keep getting 7040*pi as my answer.. but its not correct.

    please help mee!
    Last edited by calculus shmalculus; October 24th 2008 at 01:22 PM.
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  2. #2
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    The volume of a sphere is given by V=\frac{4}{3}{\pi}r^{3}

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

    You have all the info to sub into the above derivative and solve for dr/dt.

    Then, you can use that result in the surface area derivative.

    \frac{dS}{dt}=8{\pi}r\cdot \frac{dr}{dt} and solve.
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