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height increasing

Calculus I: How fast is the height of the pile increasing when the pile is 10′ high?

Gravel is being dumped from a conveyor belt at a rate of 30 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 10′ high?
How do I know what dh/dt should be.

Let v be the volume, r be the radius of the base and h be the height.
v = (1/3)pi r^2 h
Since 2r = h, substitute r = h/2,
v = (1/3)pi (h/2)^2 (h) = (1/12)pi h^3
Differentiate with respect to time,
v’ = (1/4)pi h^2 h’
Plug in h = 10, v’ = 30,
30 = 25pi h’
Solve for h’, (h’ = dh/dt)
h’ = 6/(5pi) ft/min

So, the height increases at a rate dh/dt = 6/(5pi) ft/min.

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