Water is flowing at the rate of 15 km / hour through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm? (CBSE 2011)
Here, length of the pipe = h = 15 km = 15000 m
Diameter of the pipe = 14 cm
Thus, radius of the pipe = 7 cm = 0.07 m
Now, Volume of cylindrical pipe = πr2h
= 
= 231 m3
Therefore, volume of water that is flowing through the pipe at a rate of 15km/hr is 231 m3.
Now, length of the cuboidal tank = l = 50 m
Breadth of the cuboidal tank = b = 44 m
Required height of the level of water = h’ = 21 cm = 0.21 m
Thus, volume of the cuboidal tank = lbh’
= 50 × 44 × 0.21 = 462 m3
As time required to fall 231 m3 of water in the tank = 1 hour
Thus, time required for 1m3 of water in the tank = (1/231) hour
Thus, time required for 462 m3 of water to fall in the tank = 462/231 = 2 hrs.
Therefore, 2 hours will be needed to fill the cuboidal tank up to height of 21cm.