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Rates of change

  1. Nov 13, 2008 #1
    1. The problem statement, all variables and given/known data
    Sand is falling into a conical pile at a rate of 10 cubic feet/minute. The diameter of the cone is 3 times the altitude. At what rate is the height of the pile change when the height=15feet.

    So i was going through and I dont know if i derived it wrong, but i had



    dv/dt= pi/3 R[tex]^{2}[/tex](dh/dt) * 2pi/3 R (h)

    but when i go through and solve it all with R= 3/2h I dont get the answer form the back of the book. Is my derivative wrong? I used chain rule...
  2. jcsd
  3. Nov 13, 2008 #2


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    V(t)=(1/3)pi(r(t)^2)*h(t). If you do the derivative correctly, there ought to be a dr(t)/dt hanging around someplace. And why is there a '*' between the two parts of what looks like a product rule?
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