I worked this all out, but the answers not right. I don't know if I even went about it the right way. Here's the problem:
Gravel is being dumped from a conveyor belt at a rate of 10 ft^3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 13 ft high? Give your answer correct to three decimal places.
So I know the formula for the volume of a cone is V=1/3(pi)(r^2)h, dv/dt=10ft^3/min, and h=13 ft and I have to find dh/dt. Right?
And since they say that h=diameter, I figured that I can replace the radius in the formula to h, so r^2 in the equation would be h^2/4.
Is this ok so far?