A closed tin can of a volume 16m3is to be in form of right circular cylinder,find height and radius if the least amount of material is to be used in its making

Question

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Answer 1

T.S.A. = 2(pi)r(r+h)

 

V = 16 = (pi)r²h

 

Solve the latter for h.  Substitute for h in the T.S.A. formula, giving f(r).

 

Use standard well known Calculus operations to optimize f(r). Don't forget to prove that the critical value you get is indeed the one for minimum T.S.A. for this fixed volume.