Question

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 4 liters per minute, how fast is the water level falling in centimeters per hour? [1 liter is 1000 cubic centimeters]

Answer 1

In 1 minute, 4 litre water leaves = 4*1000 cubic cm = 4000 $* (10^{-2} )^{3} m^{3}= 4000 * 10^{-6 } m^{3} = 4 *10^{-3 }m^{3}$
so, the height decrease = Volume/area =
 $\frac{4*10^{-3}}{ \pi *2^{2}} \\ = \frac{4*10^{-3}}{4*\pi} \\ = 10^{-3}/\pi = 0.318 * 10^{-3} m = 0.318 cm$
 
hence water level in cm falling per min = 0.318
hence water level in cm falling per hr= 0.318 * 60 = 19.09