Optimisation
Calculus
A soda can or a classic problem from 2014 Exams - Explore the mathematical principles and create your own unique investigation.
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
A steel-framed lobster pot with a fixed volume needs a minimum length of steel in its frame — that was an IB exam question a few years back, and it's the same idea behind a drinks can: for a fixed volume, what shape uses the least material? Work through it with a can you can actually measure, then see how far the real thing sits from your optimum.
Guiding Questions
- A drinks can holds 330 ml. What dimensions minimise the aluminium used?
- Set up volume and surface area, reduce to one variable, and find the optimum with calculus.
- Measure a real can. How far is it from your optimum, and what practical reasons might explain the gap?
- Add realistic details — thicker ends, wasted material when discs are cut from sheets. How does the optimum move?