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I know calculus can be used to calculate the dimensions of an object and the minimum material which can be used. It is a pressure vessel of a cylindrical shape.

[tex]v= \frac {4 \pi r^3} {3}[/tex]

[tex]A=2 \pi r^2 + 2 \pi rh[/tex]

as the cylinder is hollow the thickness of the walls is found by

[tex]t= \frac {pd} {4 \sigma }[/tex]

sigma = [tex]300x10^6 Nm^{-2}[/tex] (steel i think?)

p = pressure

d = diameter

I have found amount of material can be calculated by surface area multiplied by thickness but would like wo see the minimum amount of material used proved by calculus

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# Minimum material problem

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