Question

Suma tuturor muchiilor unui cub esteste de 6 radical 3cm.Calculați a) lungimea muchiei cubului b) lungimea diagonalei cubului c) volumul cubului...

Answer 1

   
[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]

Answer 2

Cubul are 12 muchii.
a) lungimea muchiei cubului:   6√3 ÷12=√3/2 cm
b) lungimea diagonalei cubului: l×√3=√3/2×√3=3/2 cm=1,5 cm
c) volumul cubului: V=l³    V=(√3/2)³    V=3√3/8 cm³