Math Problem Statement
- A map is drawn to scale 1:20000. If the actual distance between 2 cities on the map is 4.4km, find the distance between the two cities on the map giving your answer in cm.
Solution
The map scale is 1:20,000, meaning that 1 unit on the map represents 20,000 units in real life.
To find the distance on the map, follow these steps:
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Convert the actual distance to centimeters: The actual distance between the two cities is 4.4 km. We need to convert this distance into centimeters:
-
Apply the scale: The scale is 1:20,000, so the distance on the map is:
Thus, the distance between the two cities on the map is 22 cm.
Do you want more details or have any questions?
Here are 5 related questions to expand on this concept:
- If the scale was 1:10,000, what would the distance on the map be?
- How would you convert the distance if it was given in miles instead of kilometers?
- What would the actual distance be if the map distance was 10 cm on this scale?
- If a new map had a scale of 1:50,000, how would that affect the map distance for 4.4 km?
- How would the map distance change if the scale was doubled to 1:40,000?
Tip: Always ensure that units are consistent when working with scale problems, converting distances into the same units before applying the scale.
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Math Problem Analysis
Mathematical Concepts
Scale Conversion
Distance Measurement
Unit Conversion
Formulas
Distance on map = Actual distance / Scale
1 km = 1000 m
1 m = 100 cm
Theorems
Proportionality Theorem in Scale Models
Suitable Grade Level
Grades 5-7
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