Scale Factor

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. It is used to determine the ratio of the dimensions of a model or drawing to the actual object.

Front

How do you calculate the scale factor from a picture to the actual size?

Back

To calculate the scale factor, divide the actual size by the size in the picture. For example, if a picture is 3 cm and the actual size is 12 ft, convert 12 ft to cm (12 ft = 365.76 cm) and then divide: 365.76 cm / 3 cm = 121.92.

Front

If a scale drawing uses 1 inch to represent 10 feet, what is the scale factor?

Back

The scale factor is 10.

Front

What are the new dimensions of a rectangle that is scaled by a factor of 7 if the original dimensions are 2 inches by 3 inches?

Back

The new dimensions are 14 inches (2 inches x 7) and 21 inches (3 inches x 7).

Front

How do you find the actual dimensions of a room if the scale factor is 10 and the drawing dimensions are 1.25 inches by 1.5 inches?

Back

Multiply the drawing dimensions by the scale factor: 1.25 in x 10 = 12.5 feet and 1.5 in x 10 = 15 feet.

Front

What is the width of a model if the height is 20 inches and the scale factor is 2.5?

Back

The width would be 50 inches (20 inches x 2.5).

Front

If a model is scaled down by a factor of 1/4, how do you find the dimensions of the actual object?

Back

Multiply the dimensions of the model by 4 to find the actual dimensions.

Front

What is the relationship between scale factor and area?

Back

If the scale factor is k, the area of the scaled object is k^2 times the area of the original object.

Front

How do you express a scale factor as a fraction?

Back

Front

What is the scale factor if a drawing of a car is 3 inches long and the actual car is 12 feet long?

Back

The scale factor is 4 (12 feet = 144 inches, so 144 inches / 3 inches = 48).