Question

Qual o Volume de um cubo de aresta 5√3 cmg?.

Answer 1

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

         $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf V = 375\sqrt{3}\:cm^{3}\:\:\:}}\end{gathered} }$

O volume "V" do cubo é o cubo da medida da aresta "a", ou seja:

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

Se:

         $\Large\displaystyle\begin{gathered} a = 5\sqrt{3}\:cm\end{gathered}$

Então, temos:

            $\Large\displaystyle\begin{gathered}V = (5\sqrt{3})^{3} \end{gathered}$

                  $\Large\displaystyle\begin{gathered} = 5^{3}\cdot(\sqrt{3})^{3}\end{gathered}$

                  $\Large\displaystyle\text{ \begin{gathered} = 5^{3}\cdot\sqrt{3^{3}}\end{gathered} }$

                  $\Large\displaystyle\begin{gathered} = 5\cdot5\cdot5\cdot\sqrt{3\cdot3\cdot3}\end{gathered}$

                   $\Large\displaystyle\text{ \begin{gathered} = 125\cdot\sqrt{3^{2}\cdot3}\end{gathered} }$

                   $\Large\displaystyle\begin{gathered} = 125\cdot3\cdot\sqrt{3}\end{gathered}$

                  $\Large\displaystyle\begin{gathered} = 375\sqrt{3}\:cm^{3}\end{gathered}$

✅ Portanto o volume do cubo é:

             $\Large\displaystyle\begin{gathered} V = 375\sqrt{3}\:cm^{3}\end{gathered}$

                 

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