$V=\pi r^{2}H$

$a\to$ bok przekroju osiowego

$a\sqrt{2}=12|:\sqrt{2}$

$a=\frac{12}{\sqrt{2}}=\frac{12}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{12\sqrt{2}}{2}=6\sqrt{2}$

$r=\frac{a}{2}=3\sqrt{2}$

$H=a=6\sqrt{2}$

$V=\pi r^{2}H=\pi {\left(3\sqrt{2}\right)}^2\cdot 6\sqrt{2}=\pi \cdot 9\cdot 2\cdot 6\sqrt{2}=108\pi \sqrt{2}$