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Homework Help: Applications of Partial Derivatives-Cone

  1. Oct 24, 2007 #1
    [SOLVED] Applications of Partial Derivatives-Cone

    1. The problem statement, all variables and given/known data

    (Q) (Q) If a cone grows in height by dh/dt = 1 and in radius by dr/dt = 2, starting from zero, how fast is its volume growing at t =3?

    2. Relevant equations

    3. The attempt at a solution

    By applying the chain rule for partial derivatives, I obtained:

    ∂V/∂t=(2/3 πrh)(dr/dt)+(1/3 πr^2 )(dh/dt)
    However, I do not know how to proceed from here on. Please help me.
  2. jcsd
  3. Oct 24, 2007 #2


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    1. Your left hand side should be dV/dt, not partial V/partial t
    2. If h increases 1 unit/sec. and r increases 2 units/sec., what would h be in 3 seconds? What would r be in 3 secs.?
    3. Now that you know what h(3) and r(3) are, you can substitute those values along with dh/dt and dr/dt to find dV/dt.
  4. Oct 24, 2007 #3

    Ahhhh! Why didn't I see it? It was such a simple thing. :frown:
  5. Oct 24, 2007 #4
    Thanks a lot!

    Sorry I forgot to mention in my last post. Thanks a lot for your help!!!
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