To determine the plant population of maize expected on one hectare of farmland when the seeds are sown at a spacing of 60 cm by 90 cm, we need to follow a systematic approach. Let's break it down step-by-step.
Step 1: Understand the Area of One Hectare
One hectare is equivalent to 10,000 square meters (m²). This is the total area we will be working with to calculate the plant population.
Step 2: Convert Spacing from Centimeters to Meters
The spacing given is in centimeters, so we need to convert it to meters for easier calculations:
- 60 cm = 0.6 m
- 90 cm = 0.9 m
Step 3: Calculate the Area Occupied by One Maize Plant
To find out how much area one maize plant occupies, we multiply the spacing in meters:
[ \text{Area per plant} = \text{Spacing in rows} \times \text{Spacing between plants} ]
[ \text{Area per plant} = 0.6 \, \text{m} \times 0.9 \, \text{m} = 0.54 \, \text{m}^2 ]
Step 4: Calculate the Total Number of Plants per Hectare
Now, we can find out how many plants can fit into one hectare by dividing the total area of one hectare by the area occupied by one plant:
[ \text{Number of plants} = \frac{\text{Total area of one hectare}}{\text{Area per plant}} ]
[ \text{Number of plants} = \frac{10,000 \, \text{m}^2}{0.54 \, \text{m}^2} \approx 18,518.52 ]
Since we cannot have a fraction of a plant, we round this down to the nearest whole number:
[ \text{Number of plants} \approx 18,519 ]
Conclusion
The expected plant population of maize on one hectare of farmland, when sown at a spacing of 60 cm by 90 cm, is approximately
18,519 plants.
Explanation of Options
- Option A (18,519 plants): This is the correct answer based on our calculations.
- Option B (16,667 plants): This option is incorrect. It may have resulted from a miscalculation of the area per plant or misunderstanding of the spacing.
- Option C (11,111 plants): This option is also incorrect. It likely arises from an incorrect assumption about the area occupied by each plant.
- Option D (5,400 plants): This option is significantly lower than the calculated value and is incorrect. It may stem from a misunderstanding of hectare size or spacing.
Common Pitfalls
- Confusing units: Always ensure that you convert all measurements to the same unit (meters in this case) before performing calculations.
- Rounding errors: Be careful when rounding numbers; always round down when dealing with whole plants.
- Misunderstanding area calculations: Remember that the area occupied by each plant is the product of the spacing dimensions.
Revision Summary
- One hectare = 10,000 m².
- Convert spacing from cm to m for accurate calculations.
- Area per plant = spacing in rows × spacing between plants.
- Total number of plants = total area / area per plant.
By following these steps, you can accurately determine plant populations for various crops based on their spacing.