To determine the number of seedlings required to plant a 2-hectare farmland with a recommended spacing of 2.5 meters by 4.0 meters, we will follow a step-by-step approach.
Step 1: Understand the Area of the Farmland
1 hectare is equal to 10,000 square meters. Therefore, 2 hectares is:
[
2 \text{ hectares} = 2 \times 10,000 \text{ m}^2 = 20,000 \text{ m}^2
]
Step 2: Calculate the Area Required for Each Seedling
The spacing for each tree crop is given as 2.5 meters by 4.0 meters. To find the area occupied by one seedling, we multiply the two dimensions:
[
\text{Area per seedling} = \text{Spacing length} \times \text{Spacing width}
]
[
\text{Area per seedling} = 2.5 \text{ m} \times 4.0 \text{ m} = 10.0 \text{ m}^2
]
Step 3: Calculate the Total Number of Seedlings Required
To find the total number of seedlings that can be planted in the 2-hectare farmland, we divide the total area of the farmland by the area required for each seedling:
[
\text{Number of seedlings} = \frac{\text{Total area of farmland}}{\text{Area per seedling}}
]
[
\text{Number of seedlings} = \frac{20,000 \text{ m}^2}{10.0 \text{ m}^2} = 2,000
]
Conclusion
The total number of seedlings required to plant a 2-hectare farmland with the given spacing is
2,000. Therefore, the correct option is
B.
Explanation of Other Options
-
Option A (1,000): This option is incorrect because it suggests that only half the number of seedlings would be planted. This would imply that the area per seedling is larger than calculated, which is not the case.
-
Option C (10,000): This option is incorrect as it suggests that the area per seedling is much smaller than calculated. If each seedling occupied only 2 square meters, then this number could be correct, but with the given spacing, it is not.
-
Option D (20,000): This option is incorrect because it implies that each seedling occupies only 1 square meter, which contradicts the given spacing of 2.5m by 4.0m.
Common Pitfalls
- Misunderstanding Units: Ensure that you are consistent with units (meters vs. centimeters).
- Area Calculation: Always double-check the area calculation for each seedling to avoid underestimating or overestimating the space required.
- Total Area Calculation: Remember to convert hectares to square meters correctly.
Revision Summary
- 1 hectare = 10,000 m²; therefore, 2 hectares = 20,000 m².
- Area per seedling = 2.5 m × 4.0 m = 10.0 m².
- Total seedlings = Total area / Area per seedling = 20,000 m² / 10.0 m² = 2,000 seedlings.
- Correct answer is B (2,000) seedlings.