This is an activity for optimization and the Applications of Differentiation Unit in Calculus. Students are given a sheet of poster board of a specific size and are asked to create a box (with a fold-down lid) of maximum volume.
Assign students a designated poster size for whicn they will use to create a box of maximum volume.
Students should calculate the volume for two different boxes based on the orientation of the poster, either Length X Width or Width X Length. Each orientation will create a different shaped box, with different volumes.
You can decide to have them choose only the maximum volume to create, or whether to allow them to choose the shape based on their particular need.
This project can be used as a class celebration, if desired. Students can place a gift inside, wrap the box in some holiday paper (Christmas, Hanukkah, etc.)
Hope you enjoy the activity. I appreciate your feedback and suggestions.
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