Volume Similarity
This activity will explore the relationship of the scale factor on the the ratio of the side lengths versus the ratio of the volume of a rectangular prism.
- The slider represents the scale factor of the rectangle on the right to the rectangle on the left (right:left). For example, means that the side lengths have a ratio of 1:1
will allow you to create identical rectangular prisms to that of the prism on the left.
- As stated above with , the ratio of the side lengths 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 =5.
- What is the scale factor?
- What is the ratio of the sides?
- Use the
to create additional rectangular prisms of the left prism. As you create them, align them inside the prism on the right until it is filled. How many of the left prisms fit inside the right prism? What does this tell you about the ratio of the volumes of the prisms? - How does the ratio of the volumes compare to the ratio of the side lengths?
- Let's tie it all together! You have examined the relationship of the right prism to the left prism through five scale factor changes. What can you say is the relationship that exists between the scale factor and the ratio of the side lengths? What can you say is the relationship that exists between the scale factor and the ratio of the volumes?