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

Let x hours be the time taken for the pipe to fill the tank.

Since the water is flowing at the rate of 3 Km/h, Therefore,

Length of the water column in  x hours is

Therefore, the length of the pipe is

The radius of the pipe is 

Therefore, the volume of the water flowing through the pipe in x hours is

Also, Volume of the water that falls into the tank in x hours is 

We have the volume of the water flowing through the pipe in x hours = Volume of the water that falls into the tank in x hours

Thus equate equations (1) and (2)

Thus, the water in the tank will fill in 100 minutes.

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 Given that, Speed of water 

And,

 

Internal radius of the pipe 

So,

Area of cross section 

Volume of water that flows in 1 minute,

 

Let the time taken to fill the tank 

So,

Volume of water that flows in  

And,

Radius of the base of the tank 

Depth of the tank 

Volume of the cylindrical tank 

So, volume of water that flows in t minute = volume of the tank

 

Hence, the tank will be filled in 

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