Question 5
An open-top cylinder of radius r cm has volume \(64\pi\ \mathrm{cm^3}\). The material covers its base and curved side only.
Show that its material area is \(\displaystyle A= \pi r^{2}+ \frac{128\pi }{r}\), for r>0.
Find the radius that minimises the material area and prove that it gives a global minimum.
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