Question

Sand falls from a conveyor belt at the rate of 20 m^3/min. The sand forms a conical pile where the height of the cone is always 4 times the radius. How fast is the radius changing when the pile is 4 meters high?

Answer 1

volume of cone
= V = (1/3)π r^2 h, but we know h = 4r or r = h/4
V = (1/3)π (h^2/16)(h)
= (1/48)π h^3

dV = (1/16)π r^2 dr/dt
when h = 4, r = 1
20 = (1/16)π(1) dr/dt
dr/dt = 320/π m/min

check my arithmetic, did it on the screen instead of writing it out first