Scenario: Map Navigation - Use scale factors to find real distances!
You're looking at a map with a scale of 1:50,000. This means that 1 centimeter on the map represents 50,000 centimeters in real life.
Scale Formula: Actual Distance = Map Distance × Scale Factor
Scale Factor = 50,000 (the second number in the ratio)
Problem: On a map with scale 1:50,000, the distance between two cities is 2 cm. What is the actual distance?
Step 1: Identify the scale factor = 50,000
Step 2: Calculate actual distance = 2 cm × 50,000 = 100,000 cm
Step 3: Convert to meters = 100,000 cm ÷ 100 = 1,000 meters = 1 kilometer
Problem: The actual distance between two points is 1.5 km. On a map with scale 1:50,000, what is the map distance?
Step 1: Convert to centimeters = 1.5 km = 150,000 cm
Step 2: Map distance = 150,000 cm ÷ 50,000 = 3 cm
You want to draw a floor plan of your classroom using a scale of 1:100. If your classroom is 8 meters long, how long should it be on your drawing?
Solution: Drawing length = 8 meters ÷ 100 = 0.08 meters = 8 centimeters
So on your 1:100 scale drawing, the 8-meter classroom should be 8 cm long.
A map has a scale of 1:25,000. If two towns are 4 cm apart on the map, what is the actual distance in kilometers?
Your calculation:
You want to make a model of a building that is 60 meters tall. If you use a scale of 1:200, how tall should your model be in centimeters?
Your calculation: