University of Oxford Mathematician Dr Tom Crawford explains how to solve an optimisation problem used as a maths undergraduate admissions interview question.

"For a cylinder of fixed volume V=1, what aspect ratio between the radius and height gives the smallest surface area?"

This question was used by Tom for the Oxford admissions interviews in 2018.

Check your working using the Maple Calculator App – available for free on Google Play and the App Store.

Android: https://play.google.com/store/apps/details?id=com.maplesoft.companion&hl=en

Apple: https://apps.apple.com/us/app/maple-companion/id1466659419

Try another Oxford admissions interview question from 2021 here: https://youtu.be/-u6ndjpGE14

And the solution is explained here: https://youtu.be/TPJALVOkvzQ

Other videos in the Oxford Calculus series can be found here: https://www.youtube.com/playlist?list=PLMCRxGutHqflZoTY8JCm1GRzCdGXvZ3_S

Finding critical points for functions of several variables: https://youtu.be/Leomuu82-u8

Classifying critical points using the method of the discriminant: https://www.youtube.com/watch?v=5M_ts8Q2LEM

Partial differentiation explained: https://youtu.be/RVwcBGzQcT8

Second order linear differential equations: https://youtu.be/F54yhRB9qDI

Integrating factors explained: https://www.youtube.com/watch?v=ftqKuOfOX3E

Solving simple PDEs: https://youtu.be/uztjxrGY6Jw

Jacobians explained: https://www.youtube.com/watch?v=YqMelRryG8U

Separation of variables integration technique explained: https://youtu.be/zk41c0vs9XQ

Solving homogeneous first order differential equations: https://youtu.be/uqvqjbAcbL8

M.I.T. Integration Bee Question: https://youtu.be/N1IEkYMskcw

Find out more about the Maple Calculator App and Maple Learn on the Maplesoft YouTube channel: https://www.youtube.com/channel/UCq2MmZQ8-kqEVAnmL2GSMsQ

Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: https://www.seh.ox.ac.uk/people/tom-crawford

For more maths content check out Tom's website https://tomrocksmaths.com/

You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
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