Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
Sand is being dropped at the rate of 10 cubic meter per minute onto a conical pile. If the height of the pile is always twice t...Asked by ian
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?
Answers
Answered by
oobleck
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
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