Volume of Box and Total Surface Area
- Author:
- 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.