Question

Find the scale of a map if 4.2 cm on the map corresponds to an actual distance of 6.3 km.

Answer 1

The scale of the map is 1:150,000, which means that 1 cm on the map represents 150,000 cm in reality.

Step-by-step explanation:

To find the scale of a map, we need to set up a ratio that compares the map distance with the actual distance. The question provides that 4.2 cm on the map corresponds to an actual distance of 6.3 km.

First, we convert the actual distance from kilometers to centimeters for easy comparison:

• 1 km = 100,000 cm (since 1 km = 1000 meters and 1 meter = 100 cm)
• 6.3 km = 6.3 × 100,000 cm
• 6.3 km = 630,000 cm

Now, we write the scale as a ratio in the format map distance/actual distance:

Scale = 4.2 cm / 630,000 cm

To simplify the scale, we divide both the numerator and the denominator by 4.2:

• Scale = 1 / 150,000

This means that on the map, 1 cm represents 150,000 cm in reality.