Final answer:
To calculate the actual distance on the ground when given a map distance and scale, we multiply the two. For a map distance of 50 cm and a map scale of 1:250,000, the actual distance on the ground is 12,500,000 cm or 125 km.
Step-by-step explanation:
Understanding Map Scales
When working with map scales, it is crucial to understand how to convert map distances to real-world distances. A map scale defines the relationship between a distance on the map and the actual distance on the ground. Let's say we have a map where the distance between two points is 50 cm and the map scale is 1:250,000. This means that 1 cm on the map represents 250,000 cm on the ground.
To find out the actual distance on the ground, we multiply the map distance by the scale factor. In our example, we calculate the ground distance as follows:
- Scale factor: 1:250,000 (or 1 cm : 250,000 cm)
- Actual ground distance = Map distance × Scale factor
The formula becomes:
Actual ground distance = 50 cm × 250,000 cm/cm
After multiplying these two numbers together, we would find that the actual distance on the ground is 12,500,000 cm, or 125 kilometers (since 100,000 cm equals 1 kilometer).
Similarly, to solve the other example problems, you can apply the same methodology, ensuring that units are consistent and using the map scale as your guide to convert map measurements to actual distances.