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Math Help - Related rates

  1. #1
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    Related rates

    The volume V of a sphere changes with time according to the equation:
    V=35\pi + \pi t^2

    Find the rate of change of the surface area of sphere when t=1sec ?

    Am solving problems for fun
    and i really stopped at this one

    ok S=4 \pi r^2

    and V=\frac{4}{3} \pi r^3

    the problem here is that there is no value for r in the problem
    I need a start please
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  2. #2
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    Quote Originally Posted by TWiX View Post
    The volume V of a sphere changes with time according to the equation:
    V=35\pi + \pi t^2

    Find the rate of change of the surface area of sphere when t=1sec ?

    Am solving problems for fun
    and i really stopped at this one

    ok S=4 \pi r^2

    and V=\frac{4}{3} \pi r^3

    the problem here is that there is no value for r in the problem
    I need a start please
    From the chain rule:

    Can't you find r in terms of t by saying that \frac{4}{3} \pi r^3 = 35\pi + \pi t^2 which simplifies to r = \sqrt[3]{\frac{105+3t^2}{4}}

    From the chain rule

    \frac{dS}{dt} = \frac{dS}{dr} \cdot \frac{dr}{dt}<br />
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  3. #3
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    pardon
    Last edited by tom@ballooncalculus; April 19th 2010 at 06:02 AM.
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