Rectangle pool

Determine dimensions of open pool with a square bottom with a capacity 32 m3 to have painted/bricked walls with least amount of material.

Result

a =  4 m
c =  2 m

Solution:

V=32 a=b V=a2 c c=32/a2 S=a2+4ac=a2+4a(32/a2) S′=2a−128/a2 S′=0 2−128/a3=0 1−64/a3=0 a3=64 a=643=4 a=b=4 mV=32 \ \\ a=b \ \\ V=a^2 \ c \ \\ c=32/a^2 \ \\ S=a^2 +4ac=a^2 +4a (32/a^2) \ \\ S'=2a-128/a^2 \ \\ S'=0 \ \\ 2-128/a^3=0 \ \\ 1-64/a^3=0 \ \\ a^3=64 \ \\ a=\sqrt[3]{ 64 }=4 \ \\ a=b=4 \ \text{m}
c=32/a2=32/42=2 mc=32/a^2=32/4^2=2 \ \text{m}

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