a634c885-a6e5-4149-9d7a-c7530072856e 3 4 5 decimal

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Solving the cylindrical box

I hate FindRoot ! f init ε GivenFind f init ε FindRoot :

to be minimized 
for a given volume D H SurfArea 2 π D 2 / (2^* (* π D * H * + :

D H Vol π D 2^4 / * H * :

Accuracy ε 109 -^:

system H D - 0 ≡ D H Vol 5 ≡ 21 sys :

init D 0.5 ≡ H 1 ≡ 21 mat :

From educated knowledge, we know that for a given volume, the minmum surface area occurs for D = H

D H 21 mat system init ε GivenFind :

D H 21 mat 1.8534 1.8534 21 mat