Question

calcule o volume de um cubo sabendo que sua aresta mede 2 raiz de 3 cm

Answer 1

✅ Após realizar os cálculos, concluímos que o volume do referido cubo é:

  $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf V = 24\sqrt{3}\:cm^{3}\:\:\:}}\end{gathered} }$

O volume do cubo é sempre o cubo da medida da aresta, ou seja:

            $\Large\displaystyle\begin{gathered} V = a^{3}\end{gathered}$

Se:

         $\Large\displaystyle\begin{gathered} a = 2\sqrt{3}\:cm\end{gathered}$

Então, temos:

          $\Large\displaystyle\begin{gathered} V = (2\sqrt{3})^{3}\end{gathered}$

                $\Large\displaystyle\begin{gathered} = 2^{3}\cdot(\sqrt{3})^{3}\end{gathered}$

                $\Large\displaystyle\begin{gathered} = 2\cdot2\cdot2 \cdot\sqrt{3}\cdot\sqrt{3}\cdot\sqrt{3}\end{gathered}$

                $\Large\displaystyle\begin{gathered} = 8\cdot\sqrt{3\cdot3\cdot3}\end{gathered}$

                $\Large\displaystyle\text{ \begin{gathered} = 8 \cdot\sqrt{3^{2}\cdot3}\end{gathered} }$

               $\Large\displaystyle\begin{gathered} = 8\cdot3\sqrt{3}\end{gathered}$

               $\Large\displaystyle\begin{gathered} = 24\sqrt{3}\end{gathered}$

✅ Portanto, o volume do cubo é:

         $\Large\displaystyle\begin{gathered} V = 24\sqrt{3}\:cm^{3}\end{gathered}$

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