## Exam-Style Question on Optimisation## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 452. This question is similar to one that appeared on an A-Level paper (specimen) for 2017. The use of a calculator is allowed.

Moresum Soup is sold in cans with a capacities of 400ml each. Each can is in the shape of a right circular cylinder with radius \(r\) cm and height \(h\) cm.

(a) Assuming that the can is made from a metal of negligible thickness prove that the total surface area, A cm^{2}, of the can is given by the following formula:

(b) Given that r can vary, find the dimensions of a can that has minimum surface area.

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