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Calculate distances using map scales. Q. 4.1.1: If 1 cm on a map represents 5 km, what is the actual distance for 4 cm? Q. 4.1.2: If 1 cm represents 10 km, what map distance represents 125 km?

Geography

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Answer

20 km\text{20 km}

12.5 cm\text{12.5 cm}

Step-by-step solution

4 steps

Here are the solutions for questions 4.1.1 and 4.1.2.

4.1.1

  1. Determine the scale from the provided image.

    From the bar scale and ruler, we can see that 1 cm1 \text{ cm} on the ruler corresponds to 5 km5 \text{ km} in actual distance.

  2. Calculate the actual distance for a map distance of 4 cm4 \text{ cm}.

    Actual distance=Map distance×Scale factor\text{Actual distance} = \text{Map distance} \times \text{Scale factor} Actual distance=4 cm×5 km1 cm\text{Actual distance} = 4 \text{ cm} \times \frac{5 \text{ km}}{1 \text{ cm}} Actual distance=20 km\text{Actual distance} = 20 \text{ km}

    The actual distance is 20 km\boxed{\text{20 km}}.

    4.1.2

  3. Identify the given scale and real distance.

    The scale is 1 cm=10 km1 \text{ cm} = 10 \text{ km}. The real distance is 125 km125 \text{ km}.

  4. Calculate the distance that would be measured on the map.

    Map distance=Real distanceScale factor\text{Map distance} = \frac{\text{Real distance}}{\text{Scale factor}} Map distance=125 km10 km/cm\text{Map distance} = \frac{125 \text{ km}}{10 \text{ km/cm}} Map distance=12.5 cm\text{Map distance} = 12.5 \text{ cm}

    The distance measured on the map would be 12.5 cm\boxed{\text{12.5 cm}}.

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