Scale Factor

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, a quantity. It is used to enlarge or reduce a figure in a proportional way.

Front

How do you calculate the actual distance using a map scale?

Back

To find the actual distance, multiply the distance on the map by the scale factor. For example, if the scale is 1 in:100 mi and the distance on the map is 1.75 inches, the actual distance is 1.75 * 100 = 175 miles.

Front

If a building is 300 ft tall and the scale is 1 inch:10 ft, how tall is it in a scale drawing?

Back

To find the height in the scale drawing, divide the actual height by the scale factor. 300 ft / 10 ft/in = 30 inches.

Front

What is the area of a rectangle with dimensions 2.2 cm by 4.5 cm before scaling?

Back

The area is calculated by multiplying the length by the width: 2.2 cm * 4.5 cm = 9.9 cm².

Front

What happens to the area of a shape when it is enlarged by a scale factor of 4?

Back

When a shape is enlarged by a scale factor of 4, the area increases by a factor of 4² (16). If the original area is 9.9 cm², the new area will be 9.9 cm² * 16 = 158.4 cm².

Front

How do you convert a model measurement to actual size using a scale?

Back

To convert a model measurement to actual size, multiply the model measurement by the scale factor. For example, if the scale is 5 in:25 ft and the model window is 1.5 in, the actual width is 1.5 in * (25 ft / 5 in) = 7.5 ft.

Front

What is the actual distance if two cities are 3 cm apart on a map with a scale of 1 cm:5 km?

Back

To find the actual distance, multiply the distance on the map by the scale factor: 3 cm * 5 km/cm = 15 km.

Front

What is the formula for finding the new dimensions of a shape when using a scale factor?

Back

New Dimension = Original Dimension * Scale Factor.

Front

If a rectangle has a length of 4 cm and a width of 2 cm, what are the new dimensions if the scale factor is 3?

Back

New Length = 4 cm * 3 = 12 cm; New Width = 2 cm * 3 = 6 cm.

Front

What is the relationship between scale factor and similarity in geometry?

Back

Scale factors are used to determine similarity between shapes. If two shapes have the same shape but different sizes, they are similar, and their corresponding sides have a constant ratio, which is the scale factor.