Question

Gravel is being dumped from a conveyor belt at a rate of 25 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 6 ft high? (Round your answer to two decimal places.)

Answer 1

since h = 2r, r = h/2
v = pi/3 r^2h = pi/12 h^3
So,
dv/dt = pi/4 h^2 dh/dt

When h=6, we have

25 = 9pi dh/dt

Now just do the math

Answer 2

derp

Answer 3

how

Answer 4

Ayy yooo where the money at Lmao KEKW