Length, Area, Volume: Study 1 -- The Cube

**Design concept by P. Streilein
Riverside High School PLTW Engineering Program
Durham, NC**
Modeling by G. Walters

Exploring the relationships between length, area, and volume: 1. The Cube

This design could be parameterized to generate various unit cubes.
This example is a 6 unit cube (6 cm on a side) which has been separated into 6 equal slices. On each slice is labeled the Length, Width, and Depth (=1 cm). On the top face, the 1cm square units are embossed. On the bottom face are the relationships between length, area, and volume and the area and volume for the slice are calculated.

The 6 slices are stacked in the holder which shows the cumulative volume as slices are added. In the case of the 6 unit cube, these are multiples of 36. The student can either start with all of the slices in the holder and work to calculate the total volume of the cube and the remaining volumes as each slice is removed. Or, the student can start with an empty holder and build up