Question

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

Answer 1

Given:-

It is given that the canal is the shape of a cuboid with dimensions as:

• Breadth (b) = 6 m
• Height (h) = 1.5 m
• The speed of canal = 10 km/hr
• Length of canal covered in 1 hour = 10 km

To Find:-

• We need to find how much area will it irrigate in 30 minutes if 8cm of standing water is desired

step-by-step solution:-

• Length of canal covered in 60 minutes = 10 km
• Length of canal covered in 1 min = (1/60)x10 km
• Length of canal covered in 30 min (l) = (30/60)x10 = 5km = 5000 m

We know that the canal is cuboidal in shape.

Formula:-

Volume of cuboid = l x b x h

Since canal is cuboidal shape

Volume of canal = l x b x h

• = 5000x6x1.5 m³

• = 45000 m³

Now,

Volume of water in canal = Volume of area irrigated

= Area irrigated x Height

So, Area irrigated = 56.25 hectares

∴ Volume of canal = lxbxh

• 45000 = Area irrigatedx8 cm

• 45000 = Area irrigated x (8/100)m

Or, Area irrigated = 562500 m² = 56.25 hectares

Answer 2

Speed of flowing of water from canal is 10km/h , means length of water flows in 1 hour = 5 km , so length of water flows in 30 minutes = 5km

Now, volume of water flowing from canal = length of water flows in 30 minutes × breadth of canal × deep of canal

= 5000m × 6m × 1.5m = 45000 m³

Let area of field = x m²

Then, volume of water irrigates into the field = area of field × height of water during irrigation

= x m² × 8× 10⁻² m = 0.08x m³

Now, volume of water flowing from canal = volume of water in field

45000 m³ = 0.08x m³

x = 562500 m²

We know, 1 hectare = 10000 m²

So, area of field in hectare = 562500/10000 = 56.25 hectares