Question

Wheat is falling from a chute onto a level floor at a rate of 8pi ft3/min to form a conical pile. If the height of the pile is always equal to the radius of its base, at what rate is the radius increasing when the pile is 8 ft deep?

Answer 1

V = (1/3)πr^2h
but h=r
V= (1/3)πr^3
dV/dt = πr^2 dr/dt
so when h = 8 , r = 8 and dV/dt = 8π

8π = π(8)^2 dr/dt
dr/dt = 8π/(64π) = 1/8 ft/min

Answer 2

THANKS!