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How toSolve this related rates question?
Wheat falls from an overhead bin and accumulates in a conical pile, so that the radius of the base of the cone is always twice the height of the cone. If the wheat falls at a rate of 3 m3/min, how fast is the height of the wheat pile changing when the diameter of the pile is 20 meters?
1 Answer
- Iggy RockoLv 76 years agoFavorite Answer
Let r = radius, h = height, v = volume, and t = time.
r = 2h
v = pir^2 h/3 = pi(2h)^2 h/3 = 4pih^3/3
d/dt(v) = d/dt(4pih^3/3)
dv/dt = 4pih^2 (dh/dt)
When diameter = 10, height = 2.5.
3 = 4pi(2.5)^2 (dh/dt)
3 = 25pi dh/dt
dh/dt = 3/(25pi) = 0.038 m/min
