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Related rates problem (involving a cone)

  1. Oct 10, 2009 #1
    1. The problem statement, all variables and given/known data
    Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. The height of the pile is increasing at a rate of ____ feet per minute when the pile is 11 feet high.

    Recall that the volume of a right circular cone with height h and radius of the base r is given by (1/3)*pi*(r^2)*h.


    2. Relevant equations
    Noted above.


    3. The attempt at a solution
    I don't understand the problem. If the radius and the height are always the same how can they change?

    EDIT: if I am thinking of this correctly then the answer would be 0 (which is incorrect).
     
  2. jcsd
  3. Oct 10, 2009 #2

    Dick

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    It's saying the diameter and the radius both vary with time but are always equal at any given time. I.e. r=h. It isn't saying they are always the same in the sense that they are constant. Try and make an attempt again.
     
  4. Oct 10, 2009 #3
    Oh! That makes things much clearer! Thanks!
     
  5. Oct 26, 2009 #4
    Point of clarification: The problem says the diameter and HEIGHT vary with time, but they are equal to each other. So d = 2r = h, or r = 0.5h.
     
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