Question

Difficulty: EasyMap Scale Conversion and Distance Calculation

A map is drawn to a Representative Fraction (RF) scale of 1:200,0001 : 200,000. What is this scale expressed as a statement scale?

  1. 1 cm represents 2 km1\text{ cm represents } 2\text{ km}Answer
  2. B
    2 cm represents 1 km2\text{ cm represents } 1\text{ km}
  3. C
    1 cm represents 4 km1\text{ cm represents } 4\text{ km}
  4. D
    1 cm represents 20 km1\text{ cm represents } 20\text{ km}

Answer

The statement scale is 1 cm represents 2 km1\text{ cm represents } 2\text{ km}.
An RF of 1:200,0001 : 200,000 means 1 cm1\text{ cm} on the map equals 200,000 cm200,000\text{ cm} on the ground. Dividing 200,000 cm200,000\text{ cm} by 100,000100,000 converts the ground distance to 2 km2\text{ km}, yielding the statement scale of 1 cm represents 2 km1\text{ cm represents } 2\text{ km}.

Step-by-Step Solution

1
Understand the Representative Fraction (RF)
1 cm1\text{ cm} on the map represents 200,000 cm200,000\text{ cm} on the actual ground.
An RF scale of 1:200,0001 : 200,000 indicates a 1-to-200,000 ratio in identical measurement units.
2
Convert ground centimeters to meters
200,000 cm100=2,000 m\frac{200,000\text{ cm}}{100} = 2,000\text{ m}
There are 100 cm100\text{ cm} in 1 m1\text{ m}.
3
Convert ground meters to kilometers
2,000 m1,000=2 km\frac{2,000\text{ m}}{1,000} = 2\text{ km}
There are 1,000 m1,000\text{ m} in 1 km1\text{ km}.

Key Concept

Converting Representative Fraction (RF) to Statement Scale
Estimated Time:45s
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