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A map has a scale of 1:1,000,000. If the distance between two points on the map is 8 cm, what is the actual distance in kilometers?

Geography

ScanSolve AI Answer

Step-by-step solution

4 steps
  1. Measure the length of line MN on the map.

    Assuming the length of line MN as depicted in the image is 8 cm8 \text{ cm}.

  2. Calculate the actual distance in centimeters using the given scale.

    The scale of the map is 1:1,000,0001:1,000,000. This means that 1 cm1 \text{ cm} on the map represents 1,000,000 cm1,000,000 \text{ cm} in actual distance.

    Actual distance in cm=Map distance×Scale factor\text{Actual distance in cm} = \text{Map distance} \times \text{Scale factor} Actual distance in cm=8 cm×1,000,000\text{Actual distance in cm} = 8 \text{ cm} \times 1,000,000 Actual distance in cm=8,000,000 cm\text{Actual distance in cm} = 8,000,000 \text{ cm}
  3. Convert the actual distance from centimeters to kilometers.

    We know the following conversion factors:
    1 m=100 cm1 \text{ m} = 100 \text{ cm}
    1 km=1000 m1 \text{ km} = 1000 \text{ m}
    Therefore, 1 km=1000×100 cm=100,000 cm1 \text{ km} = 1000 \times 100 \text{ cm} = 100,000 \text{ cm}.

    To convert 8,000,000 cm8,000,000 \text{ cm} to kilometers, divide by 100,000 cm/km100,000 \text{ cm/km}:

    Actual distance in km=8,000,000 cm100,000 cm/km\text{Actual distance in km} = \frac{8,000,000 \text{ cm}}{100,000 \text{ cm/km}} Actual distance in km=80 km\text{Actual distance in km} = 80 \text{ km}
  4. Compare the result with the given options.

    The calculated actual distance is 80 km80 \text{ km}.
    A. 80000
    B. 8000
    C. 80
    D. 8

    The calculated value matches option C.

    The final answer is C. 80\boxed{\text{C. 80}}

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