Water in a canal, $8$ m wide and $6$ m deep, is flowing with a speed of $12$ km/hour. How much area will it irrigate in one hour, if $0.05$ m of standing water is required?
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding rag
Model Answer
Given:
- Width of canal = 8 m, Depth = 6 m
- Speed of water = 12 km/h = 12000 m/h
- Standing water required = 0.05 m
Volume of water flowing in 1 hour:
Volume = length × breadth × height
$$= 12000 \times 8 \times 6 = 576000 \text{ m}^3$$
Area irrigated:
Volume of water = Area irrigated × height of standing water
$$576000 = \text{Area} \times 0.05$$
$$\text{Area} = \frac{576000}{0.05} = 1,15,20,000 \text{ m}^2 = \mathbf{1152 \text{ hectares}}$$
Source: Chapter 12, Volume of a Combination of Solids
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Explanation
- The key idea: water flowing through the canal for 1 hour forms a cuboid of dimensions (speed × time) × width × depth. Its volume equals the volume spread over the irrigated area.
- Use Volume of canal water = Area × standing water height, then solve for Area.
- Examiners award marks for: correct volume calculation (1 mark), setting up the equation (1 mark), correct area in m² (1 mark), and converting to hectares (1 mark). Always convert to hectares at the end (1 hectare = 10,000 m²).