Question

Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour?

Answer 1

Water flows in 1 sec = 80 cm

Water flows in 1/2 hour = 80 x 3600/2 = 144000 cm

[As 1 hour = 3600 seconds]

For cylindrical pipe,

Base radius, r = 1 cm

Height, h = water flowed in half hour = 144000 cm

As we know,

Volume of cylinder = πr²h

Where r is base radius and h is height of cylinder.

Volume of water flowed through pipe = π(1)²(144000) = 144000π cm³

For cylindrical tank,

Base radius, r = 40 cm

Let the height of water raised be h cm

As we know,

Volume of cylinder = πr²h

Where r is base radius and h is height of cylinder.

Volume of water in tank = π(40)² h

144000π = 1600πh

h = 90 cm

Height of water raised in tank is 90 cm.