Gravel is being dumped from a conveyor belt at a rate of 40 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. How fast is the height of the pile increasing when the pile is 11 feet high?

Question

margotlakus · Answer

I have a few more I need help with after this one if anyone is willing to help!

mathmale · Answer

What is the formula for the volume of a cone, in terms of the base radius?  In terms of the diameter?

margotlakus · Answer

v=$$\frac{ 1 }{ 3 }\pi r^2*h$$

mathmale · Answer

Right.  We're focusing on several variables here:  cone radius (r), cone height (h), cone diameter (d).  Note that h=d always.  Thus, h=2r always.

You may need to change the variable r in your formula to (h/2).

Let the cone volume be V.  Then your label for the rate of change of the volume of the cone would be the derivative, dV/dh (rate of change of volume with respect to cone height, h).  We are not interested in the cone radius, r, or in the cone diameter, d, but are interested in the cone height, h.

So, find V as a function of h only, remembering that h=d=2r.

mathmale · Answer

Then differentiate your expression with respect to h.

mathmale · Answer

margot:  are you still interested in solving this problem?  No word from you for 35 minutes now.  ???