Question

A área total de um cubo cuja diagonal mede 4√3 cm é:

Answer 1

A diagonal de um cubo de aresta $\text{a}$ mede $\text{a}\sqrt{3}$

$\text{a}\sqrt{3}=4\sqrt{3}~\longrightarrow~\text{a}=\dfrac{4\sqrt{3}}{\sqrt{3}}~\longrightarrow~\text{a}=4~\text{cm}$

A aresta desse cubo mede $4~\text{cm}$. A área total é dada por $6a^2$

$\text{A}_{\text{T}}=6a^2$
$\text{A}_{\text{T}}=6\cdot4^2$
$\text{A}_{\text{T}}=6\cdot16$
$\text{A}_{\text{T}}=96~\text{cm}^2$

Answer 2

$a \sqrt{3} = 4 \sqrt{3} \\ \\ a = \frac{4 \sqrt{3} }{ \sqrt{3} } \\ \\ a = 4 \\ \\ logo \: teremos \\ \\ a \: area \: total \: e \\ \\ at = 6.a^{2} \\ \\ at = 6.4 ^{2} \\ \\ at = 6.16 \\ \\ at = 96m^{2}$