Question

a conveyor belt pours gravel into a pile at a rate of 20 lbs per minue. the pile is shaped like an upside-down 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!

Answer 1

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.