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Math Help - Related rate problems

  1. #1
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    Related rate problems

    The radius r of a sphere is increasing at the uniform rate of .3 inches per second. At the instant when the surface area S becomes 100pi square inches, what if the rate of increase, in cubic inches per second, in the volume V?

    s=4pir^2 v=(4/3)pir^2

    :/ All I know is a have to take the derivative of each. ><"
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  2. #2
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    you are given \frac{dr}{dt} , and the problem wants you to find \frac{dV}{dt} when the surface area = 100 \pi

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

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

    since surface area = 4\pi r^2 = 100\pi

    \frac{dV}{dt} = 100 \pi \cdot \frac{dr}{dt}

    finish up
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  3. #3
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    30 pi!
    Thank you, I was halfway through this problem when you responded. :3
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