SOLUTION: Grain pouring from a chute at the rate of 8 feet cubed per minute forms a conical pile whose altitude is always twice its radius. How fast is the altitude of the pile increasing w

Question 168043: Grain pouring from a chute at the rate of 8 feet cubed per minute forms a conical pile whose altitude is always twice its radius. How fast is the altitude of the pile increasing when the pile is 6 feet high?
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
sooo...we're now in calculus.com...

r=h/2 __ V=π(r^2)h/3 __ substituting __ V=π(h^3)/12

differentiating __ dV/dT=(π/12)(3h^2)dh/dT __ dh/dT=(dV/dT)/[(π/12)(3h^2)]

dh/dT=8/(π/4)(6^2)=32/(36π)=.283ft/min (approx)
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