Question

A \(20,000 \text{ m}^2\) maize crop field was supplied with 60 mm depth of irrigation, find out how many liters of water has gone into the field.

• A. 3 lakh
• B. 6 lakh
• C. 8 lakh
• D. 12 lakh

Hint:

A useful shortcut: An depth of \(1 \text{ mm}\) of water over an area of \(1 \text{ ha } (10,000 \text{ m}^2)\) is exactly equal to \(10,000 \text{ liters}\).
Here, the area is \(2 \text{ ha } (20,000 \text{ m}^2)\) and depth is \(60 \text{ mm}\):
\[ \text{Volume} = 2 \text{ ha} \times 60 \text{ mm} \times 10,000 \text{ liters/(ha}\cdot\text{mm)} = 1,200,000 \text{ liters} = 12 \text{ lakh liters} \]

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
To find the total volume of irrigation water applied to a field, we multiply the surface area of the field by the depth of the irrigation water layer, and then convert the volume from cubic meters to liters.
Key Formula or Approach:
The volume of water (\(V\)) is calculated as: \[ V = \text{Area } (A) \times \text{Depth } (d) \] The conversion factor from cubic meters to liters is: \[ 1 \text{ m}^3 = 1000 \text{ liters} \]

Step 2: Detailed Explanation:
Let us identify the given values and perform the calculations:

Area of the maize field, \(A = 20,000 \text{ m}^2\)

Depth of irrigation water, \(d = 60 \text{ mm} = 0.06 \text{ m}\)

Calculate the volume in cubic meters: \[ V = 20,000 \text{ m}^2 \times 0.06 \text{ m} = 1200 \text{ m}^3 \]
Convert this volume to liters: \[ V = 1200 \text{ m}^3 \times 1000 \text{ liters/m}^3 = 1,200,000 \text{ liters} \]
Express this in lakhs (where 1 lakh = 100,000): \[ V = \frac{1,200,000}{100,000} \text{ lakh} = 12 \text{ lakh liters} \] Therefore, 12 lakh liters of water was applied to the field.

Step 2: Final Answer:
The correct option is (D), representing 12 lakh.