1.
[tex]P_{c}= 54 \ cm^{2}\\oraz\\P_{c} = 6a^{2}\\\\6a^{2} = 54 \ \ /:6\\\\a^{2} = 9\\\\a = \sqrt{9}\\\\\boxed{a = 3 \ cm}[/tex]
2.
[tex]h = 4\\r = \frac{h}{2} = 2\\V = ?\\\\V = \pi r^{2}h\\\\V = \pi \cdot2^{2}\cdot 4\\\\V = \pi \cdot4\cdot4\\\\\boxed{V = 16\pi \ j^{3}}[/tex]
3.
a - krawędź szescianu
D = 3
Pc = ?
[tex]D = 3\\oraz\\D = a\sqrt{3}\\\\a\sqrt{3} = 3 \ \ /:\sqrt{3}\\\\a = \frac{3}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}} = \frac{3\sqrt{3}}{3} = \sqrt{3}\\\\\\P_{c}= 6a^{2}\\\\P_{c} = 6\cdot(\sqrt{3})^{2}\\\\P_{c} = 6\cdot3\\\\\boxed{P_{c} = 18 \ j^{2}}[/tex]
