Math Problem Statement

what is the actual number of kilometers that is represented by 5 centimeters on the map

Solution

To find the actual distance represented by 5 centimeters on a map, you need to know the map's scale. The scale tells you the ratio of map distance to actual distance.

For example:

  • If the scale is 1:100,000, this means that 1 centimeter on the map represents 100,000 centimeters in real life.
  • So, 5 centimeters on the map would represent 5×100,000=500,0005 \times 100,000 = 500,000 centimeters, which equals 5 kilometers (since 100,000 cm = 1 km).

Without the scale, it's impossible to determine the actual distance. Could you provide the map's scale?

Would you like a deeper explanation of how map scales work? Here are some questions to expand on the topic:

  1. What is the formula to convert map distances to actual distances?
  2. How does a scale of 1:50,000 compare to 1:100,000 in terms of actual distances?
  3. What other units can map scales use besides kilometers?
  4. Can a map have a variable scale depending on its region?
  5. How do you measure distances on a curved surface like Earth when using flat maps?

Tip: Always check the map's legend for the scale to ensure accurate conversions!

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Math Problem Analysis

Mathematical Concepts

Map Scales
Ratio and Proportion
Unit Conversion

Formulas

Actual Distance = Map Distance × Scale Factor
1 kilometer = 100,000 centimeters

Theorems

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Suitable Grade Level

Grades 5-7