calcule a medida da aresta de um cubo de 36 m² de area total .... Pergunta de ideia deeuDouglas

llully

✅ Após resolver os cálculos, concluímos que a medida da aresta é:

$\Large\displaystyle\text{$\begin{gathered}\boxed{\boxed{\:\:\:\bf a = \sqrt{6}\:m\:\:\:}}\end{gathered}$}$

Para calcular a aresta do cubo a partir de sua área total devemos utilizar a seguinte fórmula:

$\Large\displaystyle\text{$\begin{gathered} a = \frac{\sqrt{6 A}}{6} \end{gathered}$}$

Se:

$\Large\displaystyle\text{$\begin{gathered} A = 36\:m^{2}\end{gathered}$}$

Então, temos:

$\Large\displaystyle\text{$\begin{gathered} a = \frac{\sqrt{6\cdot36}}{6} \end{gathered}$}$

$\Large\displaystyle\text{$\begin{gathered} = \frac{\sqrt{216}}{6} \end{gathered}$}$

$\Large\displaystyle\text{$\begin{gathered} = \frac{\sqrt{6^{2}\cdot6}}{6} \end{gathered}$}$

$\Large\displaystyle\text{$\begin{gathered} = \frac{6\sqrt{6}}{6} \end{gathered}$}$

$\Large\displaystyle\text{$\begin{gathered} = \sqrt{6}\end{gathered}$}$

✅ Portanto, a medida da aresta é:

$\Large\displaystyle\text{$\begin{gathered} a = \sqrt{6}\:m\end{gathered}$}$

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