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Water flows through a circular pipe whos...

Water flows through a circular pipe whose internal diameter is 2 cm, at the rate of 0.7 m per second into a cylindrical tank, the radius of whose base is 40 cm. By how much will the level of water rise in the tank in half an hout ?

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Internal radius of the pipe, r = 1 cm.
length of water flowing in 1 second, h = 0.7 m = 70 cm.
Volume of water flowing in 1 second
`pir^(2)h=(pixx1xx1xx70) cm^(3)=(70pi)cm^(3)`
Volume of water flowing in 30 minutes
`=(70pixx60xx30) cm^(3)= (126000pi)cm^(3)`.
Radius of cylindrical tank, R = 40 cm.
Let the rise in level of water be H cm.
Volume of water in the tank.
`=piR^(2)H=(pixx40xx40xxH)cm^(3)`
`=(1600piH)cm^(3)`.
Volume of water in the tank = volume of water in the tank
`rArr" "1600piH=126000pirArrH=(126000)/(1600)=(315)/4=78.75`.
Hence, rise in level = 78.75 cm.
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