Question

Around ______________ number of plants that are required to plant 9.00 ha with an espacement of 3 m X 3 m in Quincunx planting system

• A. 7778
• B. 14446
• C. 20000
• D. 15556

Hint:

Quincunx planting almost doubles the density. If square planting gives 10,000, look for an option close to 20,000.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The Quincunx planting system involves planting in squares with an additional plant at the center of each square. This increases the total number of plants significantly compared to a standard square system.

Step 2: Key Formula or Approach:
1. Area = 9.00 ha = 90,000 m$^2$.
2. Number of plants in Square System ($n_s$) = $\frac{\text{Area}}{\text{spacing}^2}$.
3. In Quincunx, each square gets one extra plant. The total number is approximately double minus one row and one column.
4. Approx Quincunx Count $\approx$ (Square Count) + (Number of squares).

Step 3: Detailed Explanation:

• Calculate Square system count:
\[ n_s = \frac{90000}{3 \times 3} = 10000 \text{ plants} \]

• Number of rows and columns ($N$):
\[ N = \sqrt{10000} = 100 \]

• Number of squares formed:
\[ \text{Squares} = (N-1) \times (N-1) = 99 \times 99 = 9801 \]

• Total Quincunx plants = (Plants at corners) + (Plants at centers):
\[ \text{Total} = 10000 + 9801 = 19801 \]

• Among the options, 20000 is the closest approximation.

Step 4: Final Answer:
The number of plants required is around 20000.