Methods2026 NHT Exam 2 Section A · Q20CAS active1 mark

Minimum surface area of a cylindrical can

A soup company wishes to design a new can for its soup. The can must be in the shape of a cylinder with a fixed volume $V$ cm $^3$ .

In order to minimise costs, the company chooses the radius and height that minimise the total surface area of the can, which includes the base and top.

The minimum possible total surface area of the can is equal to

1 mark

\sqrt[3]{\dfrac{V}{2\pi}}

^2

\sqrt[3]{\dfrac{V}{\pi}}

^2

3\left(\sqrt[3]{\pi V^2}\right)

^2

3\left(\sqrt[3]{2\pi V^2}\right)

^2

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