Optimising the Volume of Tubes
applied
Create a constraint, e.g. the area of A4 paper and explore this classic GCSE problem from the 1990s and earlier.
Introduction
Given an A4 piece of paper, what is the maximum volume one could enclose in a 3D open-ended tube? Investigate the volume of open-ended tubes which can be made from a piece of card with a fixed area of 1200 cm². It’s a fascinating yet paradoxical solution. Remember to use tables, graphs and functions to reach a solution
Guiding Questions
- What is the objective function you want to optimize?
- What constraints apply to this problem?
- How can you use calculus to find maximum or minimum values?
- Can you verify your solution is optimal rather than a local extremum?
- How sensitive is the optimal solution to changes in parameters?
Key Mathematical Concepts
Optimization
Calculus
Engineering
Volumes of Revolution