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 level of water in the tank in half an hour.

Answer 1

See 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 $0.4\times 60\times 30$m In half an hour.

For cylindrical tank
Radius 0.4m
Let the Height be x

Now 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.