Question

The number of plants that can be accommodated with the spacing of 3 m X 3 m by following triangular system of planting in 8 ha area is

• A. 10222
• B. 11222
• C. 12222
• D. 17778

Hint:

Triangular system accommodates 15% more plants than the square system.
Square \(N = \text{Area} / S^2\).
Triangular \(N = (\text{Area} / S^2) \times 1.155\).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question requires calculating the tree density for a Triangular System of planting. This system accommodates more plants than a square system for the same spacing.
Key Formula or Approach:
For a Triangular System: \[ \text{Area per plant} = S^2 \times \frac{\sqrt{3}}{2} = S^2 \times 0.866 \] Where \(S\) is the spacing (3m). Number of plants (\(N\)) = \(\frac{\text{Total Area}}{\text{Area per plant}}\).

Step 2: Detailed Explanation:

• Area Calculation: Total Area = 8 ha = \(8 \times 10,000 = 80,000 \text{ sq.m}\).

• Area per plant calculation: Spacing \(S = 3\text{m}\). \[ \text{Area/plant} = 3^2 \times 0.866 = 9 \times 0.866 = 7.794 \text{ sq.m} \]

• Calculating Number of Plants: \[ N = \frac{80,000}{7.794} \] \[ N \approx 10264 \]

• Conclusion: Standardized values in forestry exams often use approximations or slightly different geometric rounding. Option (A) 10222 is the closest and recognized answer in this ICAR/SRF context. (Note: A square system would yield only \(80000 / 9 = 8888\) plants).

Step 3: Final Answer:
The number of plants in 8 ha at 3x3 triangular spacing is approximately 102