l=6\sqrt{6}
\alpha=45 to kąt zawarty między tworzącą l a promieniem podstawy r
V=\frac{1}{3}\Pi*r^2*h
\sin\alpha=\frac{h}{l}
h=\sin\alpha*l
sin{45}=\frac{\sqrt{2}}{2}
h=\frac{\sqrt{2}}{2}*6\sqrt{6}=3\sqrt{12}=3\sqrt{3*4}=6\sqrt{3}=
r^2=l^2-h^2
r^2=(6\sqrt{6})^2-(6\sqrt{3})^2=6^2*6-6^2*3=216-108=108
r=\sqrt{108}=6\sqrt{3}
$V=\frac{1}{3}\Pi*(6\sqrt{3})^2*6\sqrt{3}=216\sqrt{3}\Pi$$cm^3$