Math Problem Statement

The scale on a map reads 1:25000 . What would be the length in centimeters on the map for a distance if 8 km

Solution

To solve this problem, you can use the map scale to convert the real-world distance into a distance on the map.

Steps to Solve:

  1. Understand the scale: The scale 1:25000 means that 1 unit on the map corresponds to 25,000 of the same units in the real world.

  2. Convert kilometers to centimeters:

    • 1 kilometer (km) = 100,000 centimeters (cm).
    • Therefore, 8 kilometers = 8×100,000=800,0008 \times 100,000 = 800,000 centimeters.
  3. Apply the scale to find the map distance:

    • According to the scale, 125,000\frac{1}{25,000} of the real-world distance will be the map distance.
    • Map distance = 800,000 cm25,000=32\frac{800,000 \text{ cm}}{25,000} = 32 centimeters.

Answer:

The length on the map for a distance of 8 kilometers would be 32 centimeters.

Would you like more details or have any questions? Here are some related questions for practice:

  1. What would be the map distance for a real-world distance of 5 kilometers?
  2. If the map distance is 15 centimeters, what is the actual distance in kilometers?
  3. How would the map distance change if the scale was 1:50,000 instead of 1:25,000?
  4. What is the scale if 10 kilometers in the real world is represented by 40 centimeters on the map?
  5. If two points are 20 centimeters apart on the map, what is the real-world distance in meters?

Tip: Always double-check your unit conversions, especially when working with scales, to avoid errors in your calculations.

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Math Problem Analysis

Mathematical Concepts

Scale
Unit Conversion
Proportional Relationships

Formulas

Scale Formula

Theorems

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Suitable Grade Level

Grades 6-8