Question

Hello, I posted a question earlier but now I'm stuck on the second part of the question. Please help me.

Sand is being dumped from a conveyor belt at a rate of 20 cubic ft/min into a pile the shape of an inverted cone whose diameter and height are always the same.

Find the rate of increase of the radius when the pile is 20 ft. high.

Thanks.

Answer 1

As we saw earlier,

v = 1/3 pi r^2 h

Since diameter = height = 2r
h = 2r

v = pi/3 * r^2 * 2r
v = 2pi/3 r^3

dv/dt = 2pi r^2 dr/dt
20 = 2pi (10)^2 dr/dt
dr/dt = 1/(10pi)