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Given that the scale on a map is 1:480,000. Find the actual distance on the ground in kilometres by 4 centimetres on a map.

Mathematics

ScanSolve AI Answer

Answer

19.2 km19.2 \text{ km}

Step-by-step solution

3 steps
  1. Understand the map scale.

    The scale 1:480,000 means that 1 unit on the map represents 480,000 units on the ground. Since the map distance is given in centimetres, 1 cm on the map represents 480,000 cm on the ground.

  2. Calculate the actual distance in centimetres.

    The distance on the map is 4 cm.

    Actual distance in cm=4 cm×480,000\text{Actual distance in cm} = 4 \text{ cm} \times 480,000 Actual distance in cm=1,920,000 cm\text{Actual distance in cm} = 1,920,000 \text{ cm}
  3. Convert the actual distance from centimetres to kilometres.

    We know that 1 m=100 cm1 \text{ m} = 100 \text{ cm} and 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 centimetres to kilometres, divide by 100,000.

    Actual distance in km=1,920,000 cm100,000 cm/km\text{Actual distance in km} = \frac{1,920,000 \text{ cm}}{100,000 \text{ cm/km}} Actual distance in km=19.2 km\text{Actual distance in km} = 19.2 \text{ km}

    The actual distance on the ground is 19.2 km19.2 \text{ km}.

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