Question

A farmer connects a pipe of internal diameter 20 cm from a canal into

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 6 km/h, in how much time

willthe tank be filled?​

Answer 1

Answer

⇒

Radius (r

1

) of circular end of pipe =

200

20

=0.1 m

⇒Area of cross-section =π×r

1

2

=π×(0.1)

2

=0.01π sq. m

⇒Speed of water =3 kilometer per hour =

60

3000

=50 meter per minute.

⇒Volume of water that flows in 1 minute from pipe = 50×0.01π=0.5π cu. m

⇒From figure 2, Volume of water that flows in t minutes from pipe = t×0.5π cu. m

⇒Radius (r

2

) of circular end of cylindrical tank =

2

10

=5 m

⇒Depth (h

2

) of cylindrical tank =2 m

⇒Let the tank be filled completely in t minutes.

⇒The volume of water filled in tank in t minutes is equal to the volume of water flowed in t minutes from the pipe.

⇒Volume of water that flows in t minutes from pipe = Volume of water in tank

Therefore, t×0.5π=πr

2

2

×h

2

⇒t×0.5=5

2

×2

⇒t=

0.5

25×2

⇒t=100

Therefore, the cylindrical tank will be filled in

100 minute.

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