RELATED RATES, RATES, DERIVATIVES, CALCULUS

Question

At a sand and gravel plant, sand is falling off a conveyor onto a conical pile at the rate of 13 cubic feet per minute. The diameter of the base of the cone is approximately four times the altitude. At what rate is the height of the pile changing when the pile is 16ft hight?

Answer 1

Vc = Pir^2(h/3).

height and altitude are the same thing so d=4h or r=2h

so Vc=Pi((2h)^2)(h/3) = Vc=Pi(4h^2)(h/3) = Pi(h^3)(4/3)

and we have

Vc'= Pi(4/3)(3h^2)h'

we have Vc' = 13 and h = 16 so solve for h'