Comparing Similarity of Volumes
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
- 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?