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.