[tex]\texttt{Notatii:} \displaystyle\\
m = \texttt{muchia cubului} \\
d= \texttt{diagonala cubului} \\
V = \texttt{volumul cubului} \\ \\
\texttt{Rezolvare: } \\
\Sigma m = 6 \sqrt{3} \\
\texttt{a) Un cub are 12 muchii. } \\ \\
\Rightarrow ~~~m= \frac{6 \sqrt{3} }{12} = \boxed{\frac{\sqrt{3} }{2} ~cm} \\ \\
b)~~~d= \sqrt{3 m^2 } = \sqrt{3\Big(\frac{\sqrt{3} }{2}\Big)^2 }= \sqrt{3 \times \frac{3 }{4} }= \sqrt{\frac{9 }{4} }= \boxed{\frac{3}{2} ~cm}
[/tex]
[tex]\displaystyle \\
c)~~~ V = m^3 = \left(\frac{\sqrt{3} }{2} \right)^3 = \boxed{\frac{3\sqrt{3} }{8} ~cm^3 }[/tex]
