Question

A farmer connects a pipe of internal diameter 25 cm from a canal into a cylindrical tank in his field, which is 12 m in diameter and 2.5 m deep. If water flows through the pipe at the rate of 3.6 km/hr, then in how much time will the tank be filled? Also, find the cost of water if the canal department charges at the rate of ₹ 0.07 per m³.

Answer 1

we have,

the radius of the cylindrical tank, R = `12/2` = 6m = 600 cm,

the depth of the tank, H = 2.5 m = 250 cm,

the radius of the cylindrical pipe, r = `25/2` = 12.5 cm,

speed of the flowing water, h = 3.6 Km/ h `="360000 m"/"3600 s" = 100  "cm"//s`

Now,

Volume of water flowing out from the pipe in a hour = πr²h

`=22/7xx12.5xx12.5xx100  "cm"^3`

Also,

Volume of the tank = πR²H

`=22/7xx600xx600xx250  "cm"^3`

So, the time taken to fill the tank`= "Volume of the tank"/"Volume of water flowing out from the pipe"`

`= ((22/7)xx600xx600xx250)/(22/7xx12.5xx12.5xx100)`

=5760 s

`=5760/3600`

= 1.6 h

Also, the cost pof water `=0.07xx22/7xx6xx6xx2.5`

= `₹19.80`