# 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:

$V = 32 \ \\ a = b \ \\ V = a^2 \ c \ \\ c = 32/a^2 \ \\ S = a^2 +4ac = a^2 +4a (32/a^2) \ \\ S' = 2a-128/a^2 \ \\ S' = 0 \ \\ 2-128/a^3 = 0 \ \\ 1-64/a^3 = 0 \ \\ a^3 = 64 \ \\ a = \sqrt[3]{ 64 } = 4 \ \\ a=b = a = 4 = 4 \ \text { m }$
$c = 32/a^2 = 32/4^2 = 2 = 2 \ \text { m }$

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