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प्रश्न
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep. If the water flows through the pipe at the rate of 4 km/hr, then in how much time will the tank be filled completely?
उत्तर
We have,
Internal radius of the pipe, `"r" =20/2 `
Radius of the cylindrical tank, `"R" = 10/2 = 5 "m"` and
Height of the cylindrical tank , H = 2 m
Also, the speed of the water flow in the pipe, h = 4 km/hr`=(4xx1000 "m")/"1 hr" = 4000 "m/hr"`
Now,
The volume of the water flowing out of the pipe in a hour = πr2h
`= 22/7xx0.1xx0.1xx4000`
`=880/7 "m"^3`
And,
The volume of the cylindrical tank = πR2h
`=22/7xx5xx5xx2`
`=1100/7 "m"^3`
So,
The time taken to fill the tank` = "Volume of the cylindrical tank"/"Volume of water flowing out of the pipe in a hour"`
`=((1100/7))/((880/7))`
`= 1100/880`
`=5/4"hr"`
`=1(1)/4hr`
`= 1 "hr" "and" 1/4xx60min`
`= 1 "hr" 15 min`
so,the tank will be completely filled in 1 hour 15 minutes.
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