Question

a conveyor makes a conical pile of mulch which has a height that is 2/3 of the diameter
The conveyor can deliver 10 cubic yards of mulch to the pile per minute. What is the function for the height of the pile as a function of time

Answer 1

v = 1/3 π r^2 h
Now, h = 2/3 d = 4/3 r, so r = 3/4 h
v = 1/3 π (3/4 h)^2 h = 3π/16 h^3
Since v increases at a constant 10 yd^3/min,
v(t) = 10t = 3π/16 h^3
h^3 = 160t/3π
h(t) = 2∛(20t / 3π)

Answer 2

v = h * π * (3/4 h)^2 = 9/16 * π * h^3

v = 10 t

h(t) = [160 t / (9 π)]^(1/3)

Answer 3

forgot the 1/3 in the volume equation