This activity will explore the similarity between side lengths and the similarity of volumes.

The black slider represents the scale factor of the lengths of the sides of the blue rectangular prism on the right to the red rectangular prism on the left (blue:red). For example, means that the side lengths have a ratio of 1:1

Activity

As stated above with , the starting scale factor is 1:1. What is the ratio of the volumes? Why?

Move the slider to , then answer the following questions. Answer these same questions then for , , and .

What is the scale factor?

What is the ratio of the sides?

Using a calculator, what is the ratio of the volumes?

How does the ratio of the areas compare to the ratio of the sides?

Let's tie it all together! You have examined the relationship of the blue rectangular prism to the red rectangular through five scale factor changes. What can you say is the relationship that exists between the scale factor and the ratio of the sides? What can you say is the relationship that exists between the scale factor and the ratio of the areas? Do these relationships hold for integer scale factors? Try to see!