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Calculus/related rates

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Expert: - 2/24/2008


Question
Sand falls from a conveyor belt onto the top of a conical pile at a constant rate of 9 m^3/min. The height of the pile is always 5/7 of the base diameter. How fast is the height changing when the pile is 6m high? At that same instant, how fast is the base radius changing?    I think I must find V = 25/588 pi h^3, then dV/dt = 25pi/196 h^2  at which point I don’t know how to proceed. I would appreciate your help. Thank you.

Answer
The rate of fall is given, but that gives no indication of how fast the volume is increasing.

You need to know the rate at which the volume of sand is increasing from which you can determine h as a function of t.  Once this is known, the volume at time t can be found.  

dV/dt is then dV/dt = 25pi/196 h^2 dh/dt.

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