Filling a Coffee Pot

Question

A coffee pot in the form of a circular cylinder of radius 3 in. is being filled with water flowing at a constant rate. If the water level is rising at the rate of 0.8 in./s, what is the rate (in in³/s) at which water is flowing into the coffee pot? (Round your answer to one decimal place.)

Answer 1

The volume of the water is:

V = pi . r^2 . h Now get the derivative knowing that the radius of the base is fixed.

dV / dt = pi . r^2 . dh / dt = pi . 3^2 . (0.8) = 22.6 in^3/s