Boxed In and Wrapped Up
We're all familiar with cereal boxes like these, but are they the best way to package the products inside?Copyright USDA
Students review how to determine the surface area and volume of a rectangular prism, that all dimensions are equal in cubes so the volume of cubes are the length of any side raised to the third power, or cubed. This prepares them for two associated activities. First, students find the volumes and surface areas of rectangular boxes such as cereal boxes and then figure out how to convert their boxes into a new, cubical boxes having the same volume as the original. As they construct the new, cube-shaped boxes from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package items. Students consider why consumer goods are generally not packaged in cube-shaped boxes, even though this would require fewer materials and ultimately, less waste. Then, to display their findings, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. The activities involved provide valuable experience in problem solving with spatial-visual relationships.
Students learn to think like packaging engineers while considering ways in which consumer goods are boxed. They consider not only the most-efficient designs, but also how those designs will be used by the customers.
After completing this lesson, students should be able to:
- Determine the dimensions of a cube when given its volume.
- Assert that a cube has less surface area than a rectangular prism of the same volume, and then prove this assertion with examples.