# 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.

• 290

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 • 51
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