Question

The quantity of water required to irrigate one hectare area with 4 cm deep water is

• A. 4,00,000 liters
• B. 40,000 liters
• C. 4,000 liters
• D. 40,00,000 liters

Hint:

Memorize the "Irrigation Constant":
1 ha-cm = $1,00,000$ Liters.
1 ha-mm = $10,000$ Liters.
For any question, just multiply the depth in cm by $1,00,000$.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question requires a volumetric calculation of water needed to cover a specific land area (1 hectare) to a specific depth (4 cm).
Key Formula or Approach:
The volume of water is calculated by multiplying the Area by the Depth:
\[ \text{Volume} = \text{Area} \times \text{Depth} \]

Step 2: Detailed Explanation:

• Unit Conversion:
First, we must convert all units to a standard metric system (meters).
1 hectare (ha) = $10,000\text{ m}^2$
4 cm = $\frac{4}{100}\text{ m} = 0.04\text{ m}$

• Volume Calculation in Cubic Meters:
\[ \text{Volume (m}^3) = 10,000\text{ m}^2 \times 0.04\text{ m} \]
\[ \text{Volume} = 400\text{ m}^3 \]

• Conversion to Liters:
The standard conversion from cubic meters to liters is:
$1\text{ m}^3 = 1000\text{ liters}$
Therefore, the total quantity of water is:
\[ 400 \times 1000 = 4,00,000\text{ liters} \]

• Conceptual Verification:
1 hectare-mm = $10,000\text{ liters}$
1 hectare-cm = $1,00,000\text{ liters}$
Therefore, 4 hectare-cm = $4,00,000\text{ liters}$

Step 3: Final Answer:
The total volume required is $4,00,000$ liters.