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Math Help - Help With Circular Cylinder Related Rates Problem

  1. #1
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    Help With Circular Cylinder Related Rates Problem

    The diameter and height of a right circular cylinder are found at a certain instant to be 10 and 20 inches respectively. If the diameter is increasing at the rate of 1 inch per minute, what change in the height will keep the colume constant?
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  2. #2
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    V = Ah = \pi r^2h = \pi(d/2)^2h

    \frac{dV}{dt} = \pi(d/2)\frac{dd}{dt}h + \pi(d/2)^2\frac{dh}{dt}

    D/2 = r = 5, h = 10

    \frac{dV}{dt} = 100\pi\frac{dd}{dt} + 25\pi\frac{dh}{dt}

    \frac{dd}{dt} = 1

    \frac{dV}{dt} = 100\pi + 25\pi\frac{dh}{dt}

    If volume is contant, dV/dt = 0

    0 = 100\pi + 25\pi\frac{dh}{dt}
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  3. #3
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    Thanks...it makes a lot more sense now
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