Water is flowing at the rate of 15 kmh-1 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 pond rise by 21 cm?



Let the time taken by pipe to fill pond is t hours


As water flows 15 km in 1 hour, it will flow 15t meters in t hours.


Also,


Volume of cuboidal pond up to height 21 cm = Volume of water that passes through pipe in “t” hours


Now, For cuboidal pond


Length, l = 50 m


Breadth, b = 44 m


Height, h = 21 cm = 0.21 m


We know that,


Volume of tank = lbh


Where, l, b and h are the length, breadth and height of tank respectively


Volume of water = 50(44)(0.21) = 462 m3


For cylindrical pipe


Base diameter = 14 cm


Base radius, r = 7 cm = 0.07 m


[as radius = diameter/2]


Height, h = 15t km = 15000t m


[1 km = 1000 m]


As we know,


Volume of a cylinder = πr2h


Where r is base radius and h is the height of cylinder


Volume of water passed in pipe = π(0.07)2(15000t)



= 231t cm3


So, we have


231t = 462


t = 2 hours


Time required to fill tank up to a height of 25 cm is 2 hours.


8
1