A tank of water has a base a circle of radius 2 meters and vertical sides. If water leaves the tank at a rate of 6 liters per minute, how fast is the water level falling in centimeters per hour? [1 liter is 1000 cubic centimeters]

Answer 1

the cross-section has area π*200^2 cm^2
One liter = 1000 cm^3, so each minute a cylinder of height

6000/(40000π) = 3/(20π) cm

drains out.

Or, using calculus,

v = πr^2h = 40000πh
dv/dt = 40000π dh/dt
-6000 = 40000π dh/dt
dh/dt = -3/(20π) cm/min = -9 cm/hr