Water is flowing at the rate of 5 km/hour through a pipe of diameter 14 cm into a rectangular tank of dimensions 50 m × 44 m. Find the time in which the level of water in the tank will rise by 7 cm.

Given:

Diameter = 14 cm = 0.14 m

Dimensions = 50 m × 44 m

Rate = 5 km/hour

Let, the time in which the level of water in the tank rise by 7 cm = x hrs

∵ Diameter = 0.14 m

∴ Radius = 1/2 × 0.14 m = 0.07 m

∵ In one hour the water flows = 5 km

∴ In x hours the water flows(h) = 5x km = 5000x m

Volume of water flowing in x hours = πr²h

⇒ Volume of water flowing in x hours = 77 x

Volume of water falls into tank in x hours = 50 × 44 × 0.07

⇒ Volume of water falls into tank in x hours = 154 m³

Now,

Volume of water flowing in x hours = Volume of water falls into tank in x hours

⇒ 77 x = 154

Hence, the level of water in the tank will rise by 7 cm in 2 hours