In the lesson linked below, students build and enlarge a figure to learn about the relationship that the change of dimensions have on length, area, and volume. Students extrapolate to find the general formula for finding a volume when a figure is enlarged.
Lesson guidelines: http://auhsdmath.pbworks.com/w/file/fetch/75028880/Cube%20Doggie%20Dog%20.pdf
All necessary directions and handouts are in the above link. Great one or two-day lesson!