9.
[tex]D = 8 \ - \ przekatna \ szescianu\\oraz\\D = a\sqrt{3}\\\\a\sqrt{3} = 8 \ \ |:\sqrt{3}\\\\a = \frac{8}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}} = \frac{8\sqrt{3}}{3}\\\\\\V = a^{3}\\\\V = (\frac{8\sqrt{3}}{3})^{3} = \frac{512\cdot3\sqrt{3}}{27} =\frac{512\sqrt{3}}{9}\\\\\boxed{V = \frac{512\sqrt{3}}{9}}[/tex]
10.
[tex]a = 4\\h = 6[/tex]
1. Przekątna podstawy graniasłupa:
[tex]d = a\sqrt{2}\\\\\boxed{d_{p} = 4\sqrt{2}}[/tex]
2. Przekątna ściany bocznej:
[tex]d^{2} = a^{2}+b^{2}\\\\d^{2} = 4^{2}+6^{2}\\\\d^{2} = 16+36 = 52\\\\d = \sqrt{52} = \sqrt{4\cdot13}\\\\\boxed{d_{b} = 2\sqrt{13}}[/tex]
3. Przekątna graniastosłupa:
[tex]D^{2} = d_{p}^{2}+h^{2}\\\\D^{2} = (4\sqrt{2})^{2}+6^{2}\\\\D^{2} = 32 + 36 = 68\\\\D = \sqrt{68} = \sqrt{4\cdot17}\\\\\boxed{D = 2\sqrt{17}}[/tex]
