To determine the approximate length of the secondary road on the map, we need to follow a systematic approach. Here’s a detailed breakdown of how to arrive at the correct answer, which is option C (13.5 km).
Step-by-Step Explanation
- Understanding the Map Scale:
- Maps usually have a scale that indicates the relationship between distances on the map and actual distances on the ground. For example, a scale of 1:50,000 means that 1 cm on the map equals 50,000 cm (or 0.5 km) in reality.
-
Check the map for its scale. If the scale is not provided, you may need to estimate based on known distances or landmarks.
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Measuring the Road on the Map:
- Use a ruler or a piece of string to measure the length of the secondary road on the map. Let’s say you measure it to be approximately 27 cm.
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If the scale is 1:50,000, you can convert this measurement into real-world distance.
-
Calculating the Real-World Distance:
- Convert the map measurement to actual distance using the scale.
- For example, if the scale is 1:50,000, then:
[
\text{Actual Distance} = \text{Map Length} \times \text{Scale Factor}
]
[
\text{Actual Distance} = 27 \text{ cm} \times 50,000 \text{ cm/cm} = 1,350,000 \text{ cm}
]
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Convert centimeters to kilometers (since 100,000 cm = 1 km):
[
\text{Actual Distance} = \frac{1,350,000 \text{ cm}}{100,000 \text{ cm/km}} = 13.5 \text{ km}
]
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Finalizing the Answer:
- Based on the calculation, the length of the secondary road is approximately 13.5 km, which corresponds to option C.
Why Other Options Are Incorrect
-
Option A (11.5 km): This option is too short. If the road were this length, the measured length on the map would have to be significantly less than what was measured (27 cm), indicating a misunderstanding of the scale or measurement.
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Option B (12.5 km): Similar to option A, this length is also shorter than the calculated distance. It suggests an underestimation of the road's length based on the map measurement.
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Option D (10.5 km): This option is the shortest and is not plausible given the measured length of the road. It indicates a significant error in measurement or scale interpretation.
Common Pitfalls
- Misreading the Scale: Always double-check the scale of the map. A common mistake is to misinterpret the scale, leading to incorrect calculations.
- Incorrect Measurement: Ensure that the measurement is taken accurately. Using a straight edge or a flexible measuring tool can help in accurately tracing the road's path.
- Unit Conversion Errors: Be careful when converting units. Confusing centimeters with kilometers can lead to significant errors in the final answer.
Revision Summary
- Always check the map scale before measuring distances.
- Use accurate tools to measure the length of features on the map.
- Convert measurements correctly using the scale to find real-world distances.
- Be aware of common pitfalls in measurement and unit conversion to avoid errors.
By following these steps and understanding the reasoning behind the calculations, you can confidently determine the length of roads and other features on maps in future geography exams.