Question

Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80cm/ 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

Radius of the pipe $=1cm$
Rate of flow $=80$ cm/sec
Volume of water flowing in one second = πr²h = π x (1)² x 80 = 80π cm³
Volume of water flowing in one minute = 80π x 60 cm³
Volume of water flowing in 30 minutes = 80π x 60 x 30 cm³

Radius of the base of the cylindrical tank = 40 cm
Let the rise in level of the water in 30 min = 'h' cm

Volume of the water filled in 30 min = Volume of the water filled in cylindrical tank

80π x 60 x 30 = π x (40)² x h

⇒ h = 90 cm

Hence, the rise of water level in tank in half an hour = 90 cm