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/s. Determine the rise in level of water in the tank in half an hour.

Volume of water flowing through pipe in 1 sec = πR²H = π × (1)² × 0.4 × 100 cm³

Volume of water flowing through pipe in 30 mins = 30 × 60 secs = π × (1)² × 0.4 × 100 × 30 × 60

Volume of cylindrical tank in 30 mins π × 40² × h = πr²h ⇒ π × 40² × h = π × (1)² × 0.4 × 100 × 30 × 60

⇒ h = (π × (1)² × 0.4 × 100 × 30 × 60) / (π × 40²)

= (0.4 × 100 × 30 × 60) / (40 × 40)

= (40 × 30 × 60) / (40 × 40)

= 30 × 60 / 40

= 45 cm