Question

9. A farmer connects a pipe of internal diameter 20 cm from a calíal into a cylindrical tank in
her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the
rate of 3 km/h, in how much time will the tank be filled?
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Answer 1

Answer:

Internal diameter of the pipe 20cm =

100

20

=

5

1

m

Internal radius=

2

1

×

5

1

=

10

1

m

Rate of flow of water=3km/h=3000 m/h

Let the pipe take t hours to fill up the tank

volume of the water that flows in 't' hours from the pipe

= Area of cross section × speed × time

=πr

2

× speed × time

=π(

100

1

)×3000×t

=30πt

Diameter of the cylinder =10m

Depth=2m

Volume of the tank=πr

2

h=π(25)2=50πm

2

Now the volume of the water that flows from the pipe in t hours=volume of the tank

∴30πt=50π

t=

30

50

hours

t=

30

50

×60

t=100 mins

∴t=100 minutes.

Answer 2

Step-by-step explanation:

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A farmer connects a pipe of...

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A farmer connects a pipe of internal diameter 20 cm form a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 kilometer per hour, in how much time will the tank be filled?

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VIDEO EXPLANATION

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.