Sand is falling off a conveyor belt and onto a conical pile at a rate of 12 cubic feet per minute. The diameter of the base of the cone is approximately 4 times the height of the pile. A) At what rate is the height of the pile changing when the pile is 10 feet high? B) At what rate is the area of the base fo the pile changing when the pile is 10 feet high?
2 answers
What do you think it is? I cannot help you if you do not give your guess.
If the pile has height h, then its base has radius 2h, and its volume is
v = 1/3 πr^2 h = 1/3 π (2h)^2 h = 4/3 πh^3
dv/dt = 4πh^2 dh/dt
Now just plug in your numbers
v = 1/3 πr^2 h = 1/3 π (2h)^2 h = 4/3 πh^3
dv/dt = 4πh^2 dh/dt
Now just plug in your numbers
1 answer