Creating a Box
Find or create a rectangular sheet of paper, measuring 8 1/ 2 cm by 11 cm. Cut out squares from each corner as shown below. Place folds in the paper until you can form an open box. What is the length of the sides of each square that is cut out in order to create a box with maximum volume?
What restrictions are placed on the lengths of the sides of a square that is cut from the rectangle? Why are these restrictions necessary?

Extensions 
Try this exploration with a sheet of paper with a different set of dimensions. Again, this Geometer's Sketchpad template may help out. Are the results the same or different? Explain.

Related External Resources 
Cube / Rectangular Prism Activity
Activity to get students to think about the linear measurements and the corresponding area and volume measurements of the cube and the rectangular prism.
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