Mathematics — Standard (041) — CBSE Class 10 board question

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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• 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).