Question

Any crop sown at a spacing of 20cm$\times$20cm. How many number of plants will be there in one hectare area?

• A. 250,000
• B. 150,000
• C. 500,000
• D. 100,000

Hint:

To perform this calculation quickly: convert the spacing to fractions.
$20 \text{ cm} = \frac{1}{5} \text{ m}$.
Area per plant $= \frac{1}{5} \times \frac{1}{5} = \frac{1}{25} \text{ m}^2$.
Plant Population $= 10,000 \times 25 = 250,000$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Plant population calculations help farmers and agronomists determine the seed rate and spatial distribution of crops over a given area.
Key Formula or Approach:
The plant population per unit area is calculated by dividing the total land area by the area occupied by a single plant:
\[ \text{Plant Population} = \frac{\text{Total Area}}{\text{Row-to-Row Spacing} \times \text{Plant-to-Plant Spacing}} \] Where: - Total Area must be in square meters ($\text{m}^2$).
- Spacing values must be converted from centimeters ($\text{cm}$) to meters ($\text{m}$).

Step 2: Detailed Explanation:
Let us perform the calculations step-by-step:
1. Determine the total area: - 1 hectare (ha) is standardly defined as $10,000 \text{ m}^2$.
2. Convert spacing from centimeters to meters: - Row-to-Row Spacing = $20 \text{ cm} = 0.2 \text{ m}$.
- Plant-to-Plant Spacing = $20 \text{ cm} = 0.2 \text{ m}$.
3. Calculate the area occupied by a single plant: \[ \text{Area per plant} = 0.2 \text{ m} \times 0.2 \text{ m} = 0.04 \text{ m}^2 \] 4. Calculate the plant population per hectare: \[ \text{Plant Population} = \frac{10,000 \text{ m}^2}{0.04 \text{ m}^2} \] Multiplying the numerator and denominator by 100: \[ \text{Plant Population} = \frac{1,000,000}{4} = 250,000 \text{ plants} \] Thus, a spacing of $20\text{ cm} \times 20\text{ cm}$ yields exactly 250,000 plants per hectare.

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