Volume of Box and Total Surface Area
- Terry Lee Lindenmuth
Explore the volume of a box (no top) and how it is related to the total surface area.
Assumptions: A. We have a maximum surface area from an 8.5” X 11” piece of paper. B. The maximum volume will have a square base. C. The box does not have a top. Task: Build a box that has the maximum volume for a fixed surface area. Sides and bottoms must be rectangles (or squares). Use the GeoGebra applet to explore the task & answer the questions. IMP2p004BuildingBiggestLxWxH+TSAV2.ggb Questions: 1. Do all the boxes with the same surface area have the same volume? 2. Is a cube the best shape to maximize volume with the given assumptions (no top)? 3. What dimensions would create the maximum volume for the fixed surface area? 4. Draw a sketch of your results from #3. 5. Compare your results to the boxes produced by the students in your class.