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 kilometers per hour, in how much time will the tank be filled?
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Answers
Radius (r1 ) of circular end of pipe = 200/20
=0.1 m
⇒Area of cross-section =π×r¹2
=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 (h2 ) 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 ²2×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.
its the answer....
Step-by-step explanation:
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.