Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

We have the diagram of the canal as,

Given: Height of the canal = 1.5 m

Breadth of canal = 6 m

Speed of the water in the canal = 10 km/h

If speed of water = 10 km/h

⇒ In 1 hr, distance covered by water = 10 km

⇒ In 60 minutes, distance covered by water = 10 km

⇒ In 1 minute, distance covered by water = 10/60 km = 1/6 km

⇒ In 30 minutes, distance covered by water = 30 × 1/6 = 5 km = 5000 m [∵ 1 km = 1000m]

Volume of canal is given by,

Volume of canal = length × breadth × height

⇒ Volume of canal = 5000 × 6 × 1.5 [∵ length = 5000 m, breadth = 6 m & height = 1.5 m] …(i)

Now, we can understand that volume of the canal will itself be the volume of the area that needs to be irrigated. So,

Volume of the canal = Volume of the area of irrigation

⇒ 5000 × 6 × 1.5 = Area irrigated × height of irrigation

⇒ 5000 × 6 × 1.5 = Area irrigated × 8 cm

⇒ 5000 × 6 × 1.5 = Area irrigated × 8/100 m

⇒ Area irrigated =

⇒ Area irrigated = 562500 m²

Hence, it will irrigate 562500 m² area in 30 minutes, if 8 cm of standing water is needed.