E-OP01 · Least material for a closed cylinder
A closed cylinder has fixed volume \(128\pi\ \mathrm{cm^3}\), radius r cm and height h cm. Its total surface area is \(S=2\pi r^2+2\pi rh\).
Express S in terms of r only and give its feasible domain.
Find the stationary candidate and the corresponding cylinder dimensions.
Prove the candidate gives the global minimum surface area, and find that area.
Complete-answer checking, worked solutions and indicative written criteria.
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