This is an optimisation task involving finding the cylinder with the smallest surface area that has a capacity of 330 ml.

Overview of task

This is an optimisation task involving finding the cylinder with the smallest surface area that has a capacity of 330 ml.

Strands

Number; Algebra and Graphs

Prior knowledge

Students will need to know how to determine the surface area and volume of a cylinder. They will need to know how to use graphs and tables.

Relevance to Core Maths qualifications

•AQA

•C&G

•Eduqas

•Pearson / Edexcel

•OCR

Suggested approaches

This task is suitable for small group work, and provides a good opportunity to demonstrate and encourage mathematical modelling. Emphasise the idea that we capture the most important features of the situation by representing the drinks can as an ‘ideal’ cylinder; we can then move from the ‘real world’ to the ‘mathematical world’, exploring multiple representations (numeric, graphical, algebraic) of the model.

Resources/documentation

The resources provided comprise a student introduction and a PowerPoint presentation, with teacher notes.

Relevant digital technologies

Students will benefit from access to calculators, computer spreadsheets and graph-plotting software. The accompanying presentation shows some ideas for using these technologies.

Possible extensions

Students could investigate real drinks cans to see how closely they approach the optimum use of material for their capacity. They could go on to look at other forms of packaging (for example cardboard boxes) to investigate how materials are used efficiently in real-world contexts.

Acknowledgement

Inspired by Mick Blaylock of the Core Maths Support Programme.