sand is being dropped at a rate of 10cubic meters per minute onto a conical pile. if the height of the pile is always half the base radius, at what rate is the height increasing when the pile is 8m high?

Answer 1

h = 1/2 r, so r = 2h
v = 1/3 πr^2 h = 1/3 π (2h)^2 h = 4/3 πh^3
dv/dt = 4πh^2 dh/dt
4π*8^2 dh/dt = 10
dh/dt = 10/(256π) m/min