[tex]P=2\sqrt{3} \\P=\frac{a^2\sqrt{3} }{4} \\2\sqrt{3} =\frac{a^2\sqrt{3} }{4} \\2=\frac{a^2}{4} \\a^2=8\\a=\sqrt{8} \\a=2\sqrt{2} \\a=2r\\2\sqrt{2} =2r|:2\\r=\sqrt{2} \\h=\frac{a\sqrt{3} }{2} =\frac{2\sqrt{2}\cdot\sqrt{3} }{2} =\sqrt{2} \cdot\sqrt{3} =\sqrt{6} \\V=\frac{1}{3} \pi r^2\cdot h=\frac{1}{3} \pi(\sqrt{2} )^2\cdot\sqrt{6} =\frac{1}{3} \pi\cdot2\sqrt{6} =\frac{2}{3} \pi\sqrt{6}[/tex]
