[tex]V=36\sqrt{2} ~cm^{3} \\\\V=\dfrac{1}{3} \cdot P_{p} \cdot H\\\\P_{p} =a\cdot a =a^{2} ~~-podstawa~~jest~~kwadrat\\\\H-wysokosc~~ostroslupa,~~ktora~~oblicze~~z~~Tw.~~Pitagorasa~~(rysunek~~w~~zalaczniku)\\\\H^{2} +(\frac{1}{2} a)^{2} =h^{2} ~~\land~~h=\dfrac{a\sqrt{3} }{2} \\\\H^{2} +\dfrac{1}{4} a^{2} =\dfrac{3}{4} a^{2} \\\\H^{2}=\dfrac{3}{4} a^{2}-\dfrac{1}{4} a^{2}\\\\H^{2}=\dfrac{2}{4} a^{2}~~\land~~H > 0\\\\H=\dfrac{a\sqrt{2} }{2} \\\\[/tex]
[tex]\dfrac{1}{3} \cdot a^{2} \cdot \dfrac{a\sqrt{2} }{2} =36\sqrt{2} \\\\\dfrac{a^{3} \sqrt{2} }{6} =36\sqrt{2} ~~\mid \cdot \dfrac{6}{\sqrt{2} } \\\\a^{3} =36\cdot 6\\\\a^{3} =6^{2} \cdot 6\\\\a^{3} =6^{3} ~~\Rightarrow ~~a=6[/tex]
