Vocabulary

Scale Factor: A scale factor is the ratio of the lengths of two corresponding sides of two similar solids.

Concept

Determine the scale factor by comparing two similar solids.

Rules

1. Determine the scale factor.
2. To determine the scale factor, from the smaller to the larger image, place the larger image value in the numerator and the smaller image value in the denominator and simplify if necessary.
3. To determine the scale factor, from the larger to the smaller image, place the smaller image value in the numerator and the larger image value in the denominator and simplify if necessary.

Example

Drag the correct answer choice.
What is the scale factor of the larger cone to the smaller cone in the picture below?

8

$\frac{1}{8}$

18

4

Solution

To determine the scale factor, from the larger to the smaller image, place the smaller image value in the numerator and the larger image value in the denominator and simplify if necessary.

The height of the large cone is 32 and the height of the small cone is 4. 

$\frac{4}{32}$=$\frac{1}{8}$

The smaller cone is $\frac{1}{8}$ times the size of the larger cone.

Pre-requisite Skills

Dilation (8.7.4)

Area and Perimeter of Similar Figures (8.8.7)