Question

A farmer has 4000 \(\text{m}^2\) area. How much water is required for irrigation to be applied at 5 cm depth ?

• A. 2000 litre
• B. 80,000 litre
• C. 0.02 ha-m
• D. 20 \(\text{m}^3\)

Hint:

To quickly find the volume in hectare-meters (ha-m):
1. Convert Area to hectares: \(4000\text{ m}^2 = 0.4\text{ ha}\).
2. Convert Depth to meters: \(5\text{ cm} = 0.05\text{ m}\).
3. Multiply directly:
\[ \text{Volume} = 0.4\text{ ha} \times 0.05\text{ m} = 0.02\text{ ha-m} \]

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Calculating the volume of irrigation water requires multiplying the surface area of the field by the depth of water to be applied.
This volume can then be expressed in different units, such as liters, cubic meters (\(\text{m}^3\)), or hectare-meters (ha-m).
Key Formula or Approach:
The volume of water (\(V\)) is calculated as:
\[ V = \text{Area} \times \text{Depth} \]
Conversion factors to keep in mind:
- \(1\text{ ha} = 10,000\text{ m}^2\).
- \(1\text{ ha-m} = 10,000\text{ m}^2 \times 1\text{ m} = 10,000\text{ m}^3\).
- \(1\text{ m}^3 = 1,000\text{ liters}\).

Step 2: Detailed Explanation:
Let us perform the calculations step-by-step:
1. Given:
- Area, \(A = 4000\text{ m}^2\).
- Depth, \(d = 5\text{ cm} = 0.05\text{ m}\).
2. Calculate the volume in cubic meters (\(\text{m}^3\)):
\[ V = 4000\text{ m}^2 \times 0.05\text{ m} = 200\text{ m}^3 \]
(This shows that Option D, 20 \(\text{m}^3\), is incorrect).
3. Convert this volume into liters:
\[ V = 200\text{ m}^3 \times 1000\text{ liters/m}^3 = 200,000\text{ liters} \]
(This shows that Options A and B are incorrect).
4. Convert the volume into hectare-meters (ha-m):
\[ V_{\text{ha-m}} = \frac{\text{Volume in m}^3}{10,000\text{ m}^3/\text{ha-m}} \]
\[ V_{\text{ha-m}} = \frac{200}{10,000} = 0.02\text{ ha-m} \]
Therefore, the water required is exactly 0.02 ha-m.

Step 3: Final Answer:
The volume of water required is 0.02 ha-m (Option C).