This activity (download pdf here) is a variation of the "maximize the volume of the box" problems we are used to see in textbooks. It is a hands-on activity, and uses a pyramid shaped box, which leads to some very nice equations that can all be solved without a calculator. It allows students to put their learning of derivatives into practice. Students will have to build a pyramidal box and measure its volume using rice and a graduated cylinder. Then they will compare their result with the volume they find algebraically. Finally, they will apply their knowledge of calculus to find the dimensions of the box of maximum volume.
The activity is designed to use about 60 minutes of class. It can be extended depending on the feedback that is expected from the teacher, from a simple account of results to a complete reflection on the activity and description of the process.
Material to prepare for the class: Sheets of (colored) paper, scissors, glue, some rice, compasses, 2 graduated cylinders (volume 100ml), large container where students can safely pour rice into and out of their pyramids.
download pdf file here
Here are a few pyramids that were created by students, with a hole cut at the top to allow them to pour rice in.
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