✅ Após resolver os cálculos, concluímos que o volume de oito cubos iguais a partir da referida aresta é:
[tex]\Large\displaystyle\text{$\begin{gathered}\boxed{\boxed{\:\:\:\bf V_{8\,c} = 512x^{6}y^{3}\,\,u.\,v.\:\:\:}}\end{gathered}$}[/tex]
Seja a aresta:
[tex]\Large\displaystyle\text{$\begin{gathered} a = 4x^{2}y\end{gathered}$}[/tex]
Sabemos que o volume de um cubo pode ser montado coma seguinte fórmula:
[tex]\Large\displaystyle\text{$\begin{gathered} \bf(I)\end{gathered}$}[/tex] [tex]\Large\displaystyle\text{$\begin{gathered} V = a^{3}\end{gathered}$}[/tex]
Como queremos calcular o volume de 8 cubos - supostamente iguais - devemos fazer:
[tex]\Large\displaystyle\text{$\begin{gathered} \bf(II)\end{gathered}$}[/tex] [tex]\Large\displaystyle\text{$\begin{gathered} V_{8\,c} = 8V\end{gathered}$}[/tex]
Substituindo "I" em "II", temos:
[tex]\Large\displaystyle\text{$\begin{gathered} \bf(III)\end{gathered}$}[/tex] [tex]\Large\displaystyle\text{$\begin{gathered} V_{8\,c} = 8\cdot a^{3}\end{gathered}$}[/tex]
Substituindo o valor de "a" na equação "III", temos:
[tex]\Large\displaystyle\text{$\begin{gathered} V_{8\,c} = 8\cdot\left[(4x^{2}y)^{3}\right]\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = 8\cdot \left[4^{3}\cdot x^{2\cdot3}\cdot y^{3}\right]\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = 8\cdot \left[64x^{6}y^{3}\right]\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = 8\cdot 64x^{6}y^{3}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = 512x^{6}y^{3}\end{gathered}$}[/tex]
✅ Portanto, o volume de oito cubos é:
[tex]\Large\displaystyle\text{$\begin{gathered} V_{8\,c} = 512x^{6}y^{3}\,\,u.\,v.\end{gathered}$}[/tex]
Saiba mais:
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✅ Após resolver os cálculos, concluímos que o volume de oito cubos iguais a partir da referida aresta é:
[tex]\Large\displaystyle\text{$\begin{gathered}\boxed{\boxed{\:\:\:\bf V_{8\,c} = 512x^{6}y^{3}\,\,u.\,v.\:\:\:}}\end{gathered}$}[/tex]
Seja a aresta:
[tex]\Large\displaystyle\text{$\begin{gathered} a = 4x^{2}y\end{gathered}$}[/tex]
Sabemos que o volume de um cubo pode ser montado coma seguinte fórmula:
[tex]\Large\displaystyle\text{$\begin{gathered} \bf(I)\end{gathered}$}[/tex] [tex]\Large\displaystyle\text{$\begin{gathered} V = a^{3}\end{gathered}$}[/tex]
Como queremos calcular o volume de 8 cubos - supostamente iguais - devemos fazer:
[tex]\Large\displaystyle\text{$\begin{gathered} \bf(II)\end{gathered}$}[/tex] [tex]\Large\displaystyle\text{$\begin{gathered} V_{8\,c} = 8V\end{gathered}$}[/tex]
Substituindo "I" em "II", temos:
[tex]\Large\displaystyle\text{$\begin{gathered} \bf(III)\end{gathered}$}[/tex] [tex]\Large\displaystyle\text{$\begin{gathered} V_{8\,c} = 8\cdot a^{3}\end{gathered}$}[/tex]
Substituindo o valor de "a" na equação "III", temos:
[tex]\Large\displaystyle\text{$\begin{gathered} V_{8\,c} = 8\cdot\left[(4x^{2}y)^{3}\right]\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = 8\cdot \left[4^{3}\cdot x^{2\cdot3}\cdot y^{3}\right]\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = 8\cdot \left[64x^{6}y^{3}\right]\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = 8\cdot 64x^{6}y^{3}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} = 512x^{6}y^{3}\end{gathered}$}[/tex]
✅ Portanto, o volume de oito cubos é:
[tex]\Large\displaystyle\text{$\begin{gathered} V_{8\,c} = 512x^{6}y^{3}\,\,u.\,v.\end{gathered}$}[/tex]
Saiba mais: