Question

Water is flowing through a cylindrical pipe of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m per second. Determine the rise in lvel of water in the tank in half an hour.

Answer 1

Since the volume of water which passes through the cylindrical pipe is equal to the volume of water present in the cylindrical tank after half an hour.

So volume will remain conserved.

For cylindrical pipe
Radius 0.01m
Height 0.4m/s ie $0.4\times 60\times 30m$ In half an hour.

For cylindrical tank
Radius 0.4m
Let x be the height

V1=V2
$3.14\times (0.01{)}^2\times 720=3.14\times (0.4{)}^2\times x$
Solving for x
We get x=45cm.