Sand falls from a conveyor belt at the rate of 10m^3/min onto the top of a conical pile. The height of the pile is always 3/8ths of the base diameter.
How fast is the radius changing when the pile is 4 m high?
3. The Attempt at a Solution
V = pir^2 (4/3) -- volume of a cone
dv/dt = (4pi/3)(2r)(dr/dt)
10 = (4pi/3)(2)(16/3)(dr/dt)
10 = (128pi/9)(dr/dt)
dr/dt = 0.224
The answer is 0.1119 m/sec. What am I doing wrong?