Real-world examples of scale factors for enlargements and reductions

📚 Quick Study Guide

• 📐 Scale Factor Definition: A scale factor is the ratio between corresponding measurements of an object and a representation of that object (an enlargement or reduction).
• ➕ Enlargement: If the scale factor is greater than 1, the object is enlarged.
• ➖ Reduction: If the scale factor is between 0 and 1, the object is reduced.
• 📏 Calculating Scale Factor: Scale factor = (Dimension of the new shape) / (Dimension of the original shape)
• 🗺️ Real-World Applications: Scale factors are used in maps, models, blueprints, and image resizing.
• 💡 Important Note: Units must be consistent when calculating scale factors.

Practice Quiz

1. What scale factor is used to enlarge a 5cm square to a 15cm square?
   1. A) 0.33
   2. B) 3
   3. C) 10
   4. D) 20
2. A map has a scale of 1:50000. Two cities are 4cm apart on the map. What is the actual distance between them in kilometers?
   1. A) 2 km
   2. B) 20 km
   3. C) 200 km
   4. D) 0.2 km
3. A photo is reduced by a scale factor of 0.5. If the original photo was 10cm wide, what is the width of the reduced photo?
   1. A) 20cm
   2. B) 5cm
   3. C) 15cm
   4. D) 2.5cm
4. An architect is creating a model of a building using a scale factor of 1:200. If the building is 30 meters tall, how tall is the model in centimeters?
   1. A) 1.5cm
   2. B) 6cm
   3. C) 15cm
   4. D) 60cm
5. A microorganism is enlarged by a microscope with a scale factor of 500. If the microorganism appears to be 2mm long under the microscope, what is its actual length in micrometers ($\mu m$)? (1 mm = 1000$\mu m$)
   1. A) 4 \$\mu m$
   2. B) 2.5 \$\mu m$
   3. C) 0.4 \$\mu m$
   4. D) 25 \$\mu m$
6. A square has an area of 9 cm². It is enlarged by a scale factor of 2. What is the area of the enlarged square?
   1. A) 18 cm²
   2. B) 36 cm²
   3. C) 27 cm²
   4. D) 81 cm²
7. A circle with a radius of 4cm is reduced by a scale factor of 0.25. What is the radius of the reduced circle?
   1. A) 1cm
   2. B) 16cm
   3. C) 0.16cm
   4. D) 2cm