calculus word problem
posted by Anonymous .
a conveyor belt pours gravel into a pile at a rate of 20 lbs per minue. the pile is shaped like an upsidedown cone. the proportions of the cone are such that when the pile is complete, the diameter of the base is 6 ft and the height is 10 feet. how fast is the height of the pile changing when the pile is 7 ft high?
I keep getting stuck!

let the radius be r and the height be h
Assuming the cone maintains the same shape
2πr=6
r = 3/π
and r/h = (3/π)/10
r = 3h/(10π)
V = (1/3)πr^2 h
= (1/3)π(9h^2/(100π^2))h
= 3h^3/(100π)
dV/dt = (9/100π)h^2 dh/dt
At this point you will have to know what the relationship between lbs of concrete and cubic feet is, I work in metric and no longer know those units.
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