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Math Help - rate of change

  1. #1
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    rate of change

    A machine is rolling metal cylinder under pressure. The radius of the cylinder is decreasing at a constant rate of 0.05 inches per second and the volume V is 128  \pi cubic inches. At what rate is the length H changing when the radius r is 2.5 inches?  [Hint: V = \pi r^2 h]
    Last edited by Samantha; August 22nd 2007 at 12:51 PM.
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  2. #2
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    Quote Originally Posted by Samantha View Post
    A machine is rolling metal cylinder under pressure. The radius of the cylinder is decreasing at a constant rate of 0.05 inches per second and the volume V is 128  \pi cubic inches. At what rate is the length H changing when the radius r is 2.5 inches?  [Hint: V = \pi r^2 h]
    Use your hint.

    Note: It would help if you could post in a less general category and profide a more descriptive title. It might give a clue as to your level or what class you are in or what tools should be used.

    In this case, it's a nice differential calculus problem. If you're in a different class, that will be a problem.

    r and h are functions of time.
    V is constant, so dV = 0
    dr is given as -0.05"/sec
    Find dh when r = 2.5"

    Complete derivative:

    V = \pi r^2 h

    dV = \pi \left(r^{2}\frac{dh}{dt} + h*\left(2r\frac{dr}{dt}\right)\right)

    dV is known.
    r is given.
    dh/dt is what we need. We'll have to solve for it after everything else is found.
    h - You will have to solve for this from the Hint.
    dr/dt is given.
    Substitute and solve.

    Additional Note: Please show your work. It is a great place to learn where you are in your mathematics understanding.
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  3. #3
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    It's calc...I'mnot sure what to do =(
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  4. #4
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    Quote Originally Posted by Samantha View Post
    It's calc...I'mnot sure what to do =(
    Samantha, Samantha...I did nearly the entire problem for you. It is time for you to start showing a little more gumption. Please go read the previous post and pick out the statements that contain instructions for you to follow.

    Really, there remains only a little algebra. If you cannot do it, you should go have a really frank conversation with your academic advisor.
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