**Geometry 12.7 Similar Solids**

**Similar sol**ids - two solids with equal ratios of corresponding linear measures, such as heights or radii.

Common ratio is called the **scale factor**.

Example:

If a rectangular prism has sides of 3, 2, and 2, and a second one has lengths of 5, 4, and 4, are these two solids similar?

Set up ratios:

3/6 = 2/4 = 2/4

1/2 = 1/2 = 1/2 , so yes they are.

If 2 similar solids have a scale factor of a:b, then the corresponding areas have a ratio of a^{2}:b^{2} and corresponding volumes have a ratio of a^{3}:b^{3}.

Example:

If one sphere has a volume = 8*pi *and a second one has a volume of 125*pi*, what is the ratio of their areas?

((8*pi*)/(125*pi*))^{1/3} = 2/5

(2/5)^{2} = **4/25**

Example:

The scale factor of the model car is 1:16. If the model car is 5.5 in. What is the height of the car?

1/16 = 5.5/x

x = 88 inches

Homework: Worksheet 12.7 B