To calculate the expected plant population of okro (also known as okra) seeds sown on a specific area of farmland, we need to follow a systematic approach. Let's break down the problem step-by-step.
Step 1: Understand the Area and Spacing
- Area of farmland: 0.72 hectares
- Spacing between plants: 60 cm
Step 2: Convert Area to Square Meters
1 hectare is equal to 10,000 square meters. Therefore, to convert 0.72 hectares to square meters:
[
0.72 \text{ hectares} = 0.72 \times 10,000 \text{ m}^2 = 7,200 \text{ m}^2
]
Step 3: Calculate the Planting Density
The spacing of 60 cm means that each plant occupies a certain area. To find out how many plants can fit in a square meter, we first convert the spacing from centimeters to meters:
[
60 \text{ cm} = 0.6 \text{ m}
]
Now, the area occupied by one plant can be calculated as:
[
\text{Area per plant} = \text{Spacing} \times \text{Spacing} = 0.6 \text{ m} \times 0.6 \text{ m} = 0.36 \text{ m}^2
]
Step 4: Calculate the Number of Plants per Square Meter
To find out how many plants can be planted in one square meter, we take the reciprocal of the area occupied by one plant:
[
\text{Number of plants per m}^2 = \frac{1}{\text{Area per plant}} = \frac{1}{0.36 \text{ m}^2} \approx 2.78 \text{ plants/m}^2
]
Step 5: Calculate the Total Plant Population
Now, we can calculate the total expected plant population by multiplying the number of plants per square meter by the total area in square meters:
[
\text{Total plant population} = \text{Number of plants per m}^2 \times \text{Total area in m}^2
]
[
\text{Total plant population} = 2.78 \text{ plants/m}^2 \times 7,200 \text{ m}^2 \approx 20,016 \text{ plants}
]
Since we typically round to the nearest whole number, we can say the expected plant population is approximately
20,000 plants.
Conclusion: Correct Option
The correct option is
D. 20,000 plants.
Explanation of Other Options
- A. 3,600 plants: This number is too low. It does not account for the area effectively and suggests a much larger spacing or fewer plants than calculated.
- B. 7,200 plants: This option suggests that one plant is placed per square meter, which is incorrect given the spacing of 60 cm.
- C. 10,000 plants: This option also underestimates the number of plants, as it implies a spacing that is not consistent with the given 60 cm.
Revision Summary
- To find plant population, convert area to square meters and calculate the area occupied by each plant based on spacing.
- Use the formula: Total plant population = (Number of plants per m²) × (Total area in m²).
- The expected plant population for okro seeds sown at 60 cm spacing on 0.72 hectares is approximately 20,000 plants.
- Always check calculations and ensure units are consistent throughout the process.