Question

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep. If the water flows through the pipe at the rate of 4 km/hr, then in how much time will the tank be filled completely?

Answer 1

We have,

Internal radius of the pipe, `"r" =20/2 `

Radius of the cylindrical tank, `"R" = 10/2 = 5 "m"` and

Height of the cylindrical tank , H = 2 m

Also, the speed of the water flow in the pipe, h = 4 km/hr`=(4xx1000 "m")/"1 hr" = 4000   "m/hr"`

Now,

The volume of the water flowing out of the pipe in a hour = πr²h 

`= 22/7xx0.1xx0.1xx4000`

`=880/7 "m"^3`

And,

The volume of the cylindrical tank = πR²h 

`=22/7xx5xx5xx2`

`=1100/7 "m"^3`

So, 

The time taken to fill the tank` = "Volume of the cylindrical tank"/"Volume of water flowing out of the pipe in a hour"`

`=((1100/7))/((880/7))`

`= 1100/880`

`=5/4"hr"`

`=1(1)/4hr`

`= 1  "hr"  "and" 1/4xx60min`

`= 1  "hr"  15 min`

so,the tank will be completely filled in 1 hour 15 minutes.