Question

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 ?

Answer 1

Given, length of the pond = 50 m and width of the pond = 44 m
Depth required of water = 21 cm `= (21)/(100) m`
`therefore` Volume of water in the pond `= (50 xx 44 xx (21)/(100)^(3) = 462 m^(3))`
Also,given radius of the pipe = 7 cm `= (7)/(100)m`

and speed of water flowing through the pipe `= (15 xx 100) = 15000 mh^(-1)`
Now, volume of water flow in 1 h `= pi R^(2)H`
`= ((22)/(7) xx (7)/(100) xx (7)/(100) xx 15000)`
`= 231 m^(3)`
Since, `231 m^(3)` water falls in the pond in 1 h.
So, `1 m^(3)` water falls in the pond in `(1)/(231)h`.
Also, `462 m^(3)` of water falls in the pond in `((1)/(231) xx 462) h = 2h`
Hence, the required time is 2 h.