Question

A 5 ha wheat crop field was supplied with 6 cm depth of irrigation, compute how many liters of water has gone into the field.

• A. 3 lakh
• B. 5 lakh
• C. 5 lakh
• D. 9 lakh

Hint:

Use this standard conversion shortcut:
\[ 1 \text{ hectare-cm (ha-cm)} = 100,000 \text{ Litres (1 Lakh Litres)} \] Here, we have:
\[ 5 \text{ ha} \times 6 \text{ cm} = 9 \text{ ha-cm} \] \[ \text{Volume} = 9 \times 100,000 \text{ L} = 900,000 \text{ L (9 Lakh Litres)} \] This makes the calculation extremely fast.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
To calculate the total volume of water applied to a field, we multiply the surface area of the field by the depth of the irrigation water.
Key Formula or Approach:
Volume of water (\(V\)) is:
\[ V = \text{Area} \times \text{Depth} \] Conversion factors:
- \(1 \text{ hectare (ha)} = 10,000 \text{ m}^2\)
- \(1 \text{ m}^3 = 1000 \text{ litres}\)

Step 2: Detailed Explanation:
Let us perform the calculations step-by-step:
Convert the area to square meters:
Given Area = \(5 \text{ ha}\).
\[ \text{Area} = 5 \times 10,000 \text{ m}^2 = 15,000 \text{ m}^2 \] Convert the irrigation depth to meters:
Given Depth = \(6 \text{ cm}\).
\[ \text{Depth} = \frac{6}{100} \text{ m} = 0.06 \text{ m} \] Calculate the volume of water in cubic meters (\(m^3\)):
\[ \text{Volume} = 15,000 \text{ m}^2 \times 0.06 \text{ m} = 900 \text{ m}^3 \] Convert the volume to litres:
\[ \text{Volume in Litres} = 900 \text{ m}^3 \times 1000 \text{ L/m}^3 = 900,000 \text{ Litres} \] Thus, 900,000 litres (9 lakh litres) of water was applied to the field.

Step 3: Final Answer:
The correct option is (D).