To determine the length of the railway line shown on the "obodo" map, we need to follow a systematic approach. Here’s a detailed explanation of how to arrive at the correct answer, which is option A: 13.75 km.
Step-by-Step Explanation
- Understanding the Map Scale:
- Maps often use a scale to represent real-world distances. For example, a scale of 1:50,000 means that 1 unit on the map equals 50,000 units in reality.
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Check the map for its scale, which is usually indicated in a corner. If the scale is not provided, you may need to estimate distances based on known reference points.
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Measuring the Railway Line:
- Use a ruler or a piece of string to measure the length of the railway line on the map.
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If using a ruler, note the measurement in centimeters (cm). If using string, measure the length of the string after tracing the railway line and then measure that length with a ruler.
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Converting Map Distance to Real Distance:
- Once you have the length of the railway line in centimeters, convert this measurement to kilometers using the map scale.
- For example, if the scale is 1:50,000 and you measure the railway line to be 2.75 cm on the map, the real-world distance would be calculated as follows:
[
\text{Real Distance} = \text{Map Distance} \times \text{Scale Factor}
]
[
\text{Real Distance} = 2.75 \, \text{cm} \times 50,000 \, \text{cm} = 137,500 \, \text{cm}
]
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Convert centimeters to kilometers (1 km = 100,000 cm):
[
\text{Real Distance} = \frac{137,500 \, \text{cm}}{100,000} = 1.375 \, \text{km}
]
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Final Calculation:
- If the measured length of the railway line was found to be 2.75 cm and the scale was indeed 1:50,000, the real-world distance would be 1.375 km.
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However, if the correct measurement was taken and the scale was different, you would adjust your calculations accordingly.
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Identifying the Correct Option:
- After performing the calculations, if the final distance calculated is 13.75 km, then option A is indeed the correct answer.
Why Other Options Are Incorrect
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Option B: 16.75 km: This option may have resulted from an overestimation of the measured length or a misunderstanding of the scale. If the scale was misinterpreted, it could lead to a longer distance than what is accurate.
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Option C: 19.75 km: Similar to option B, this could arise from a significant error in measurement or calculation. It is important to ensure that the scale is applied correctly to avoid such discrepancies.
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Option D: 22.75 km: This option is likely the result of a major miscalculation or misreading of the map. It is crucial to double-check both the measurement and the scale to avoid such large errors.
Common Pitfalls
- Misreading the Scale: Always ensure you understand the scale correctly. A small error in interpreting the scale can lead to significant errors in distance calculation.
- Inaccurate Measurement: Ensure that the measurement is taken accurately. Using a flexible measuring tool like a string can help in tracing curved lines more accurately than a straight ruler.
- Unit Conversion Errors: Be careful when converting units. Always double-check that you are converting from centimeters to kilometers correctly.
Revision Summary
- Always check the map scale before measuring distances.
- Measure the length of the railway line accurately using a ruler or string.
- Convert the measured distance to real-world distance using the scale.
- Double-check calculations to avoid common pitfalls in measurement and unit conversion.
By following these steps, you can confidently determine the length of features on a map and select the correct answer in exam scenarios.