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Math Help - Need help with related rate problem.

  1. #1
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    Need help with related rate problem.

    How fast is the surface area of a spherical balloon increasing if the radius is 7 in and the volume is increasing at the rate of 5 cu in/sec?

    I'm not sure how to solve this one as S=4*pi*r^2 does not take into account volume.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by swatpup32 View Post
    How fast is the surface area of a spherical balloon increasing if the radius is 7 in and the volume is increasing at the rate of 5 cu in/sec?

    I'm not sure how to solve this one as S=4*pi*r^2 does not take into account volume.
    You do know that

    V=\frac{4}{3}\pi r^3 so taking the deriviative with respect to t gives

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

    We were given that value of \frac{dV}{dt}=5

    so we can solve for \frac{dr}{dt}

    This should get you started, happy hunting
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  3. #3
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    So the dr/dt from v = 4/3*pi*r^3 will be the input for dr/dt from s=4*pi*r^2.

    correct?
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by swatpup32 View Post
    So the dr/dt from v = 4/3*pi*r^3 will be the input for dr/dt from s=4*pi*r^2.

    correct?
    Exactly!!
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