Question

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/hr, in how much time will the tank be filled

Answer 1

It takes 100 minutes to fill the tank.

Explanation:

Let the length of the pipe used for filling the tank be h

Then

Volume of the pipe = volume of the tank

Step 1: Finding the volume of the pipe

The pipe is in cylindrical form with height h and diameter 20m

The volume of the pipe =
`\pi r^2h`

Where r is the radius of the pipe

r =
`(diameter)/(2)`

r =
`(20)/(2)`

r = 10cm =
`(1)/(10)`

The volume of the pipe

=>
`\pi ((1)/(10))^2 h`

=>
`(1)/(100)\pi h`

=>
`(\pi h)/(100)`-----------------------------------(1)

Step 2: Finding the volume of the tank

The volume of the tank =
`\pi r^2h`

Where r is the radius of the tank

r =
`(diameter)/(2)`

r =
`(10)/(2)`

r = 5

The volume of the pipe

=>
`(\pi )(5)^2 (2)`

=>
`50 \pi`-------------------------------------(2)

Equating (1) and (2)

`(\pi h)/(100)` =
`50 \pi`

`(h)/(100)` = 50

h = 50 X 100

h =5000m =5km

The flow rate of water through the pipe = 3 km/hr

time taken to travel 3 km = 1 hours

so time taken 1 km =
`(1)/(3)` hours

To Travel 5 km

=>
`5 * (1)/(3)` hours

=>
`(5)/(3)` hours

converting into minutes

=>
`(5)/(3) * 60`

=>
`(300)/(3)`

=> 100 minutes