Scale Factors and Proportions in Geometry

This lesson covers the concept of scale and scale factor, using examples such as model airplanes and clay models. It explains how to calculate dimensions using proportions and scale factors, and applies these concepts to similar triangles and rectangular prisms. The lesson demonstrates how scale affects area and volume, providing a comprehensive understanding of these mathematical principles.

What is the scale factor used in the model airplane example?

• 1 to 48

• 1 to 36

• 1 to 24

• 1 to 12

If a model airplane has a wingspan of 18 inches, what is the wingspan of the actual airplane in feet?

• 36 feet

• 30 feet

• 42 feet

• 24 feet

What is the purpose of using a ratio box in scale problems?

• To simplify calculations

• To avoid errors

• To check units

• To visualize proportions

How many inches tall should Sophia's model car be if the actual car is 54 inches tall and the scale is 1 to 36?

• 2.5 inches

• 2 inches

• 1.5 inches

• 1 inch

What is the scale factor if 3 over 7 equals 15 over n?

• 25

• 30

• 40

• 35

How do you calculate the scale factor from a smaller triangle to a larger triangle?

• Subtract the smaller side from the larger side

• Add the sides together

• Multiply the smaller side by the larger side

• Divide the larger side by the smaller side

What is the scale factor from a smaller rectangular prism to a larger one if one side is 2 cm and the corresponding side is 6 cm?

• 5

• 4

• 3

• 2

If the scale factor is 3, how many times larger is the volume of the larger prism compared to the smaller one?

• 36 times

• 27 times

• 18 times

• 9 times