# Optimization using calculus [closed]

A typical chips and crepe packaging cone, for example, has V = 355 cm3.) What dimensions (height and radius) will minimize the cost of recycled paper to construct the cone?

## closed as off-topic by max_zorn, GNUSupporter 8964民主女神 地下教會, Ak19, Thomas Shelby, Lord Shark the UnknownJun 16 at 5:50

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• For homework problems it is generally expected that some marginal effort will be spent on a solution... – copper.hat Jun 6 at 13:25
• Make the entire cone of non-recycled paper. Guaranteed minimum. – Henning Makholm Jun 6 at 13:26

You will need the formula for the surface area, which is given by $$M=\pi r\sqrt{r^2+h^2}+\pi r^2$$ and the formula for the volume $$V=\frac{1}{3}\pi r^2h$$ so we have to optimize the function $$g(r)=\pi r\sqrt{r^2+\left(\frac{3V}{\pi r^2}\right)^2}+\pi r^2$$