Question

A aresta de um cubo é 2 raiz de 3cm. Calcular a diagonal, a área total e o volume desse cubo.

Answer 1

$Diagonal~do~cubo ~ \\ \\ \\ D = a \sqrt{3} \\ \\ D = (2 \sqrt{3)} . \sqrt{3} \\ \\ D = 2 . ( \sqrt{3} )^2 \\ \\ D = 2 . 3 \\ \\ D = 6 ~cm$

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$Area ~total \\ \\ At = 6. a^2 \\ \\ At = 6. (2 \sqrt{3})^2 \\ \\ At = 2^2 . ( \sqrt{3)^2} \\ \\ At = 4 . 3 \\ \\ At = 12 ~cm^2$


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$Volume: \\ \\ V = (2 \sqrt{3})^3 \\ \\ V = 2^3. ( \sqrt{3}) ^3 \\ \\ V = 8 . 3 . \sqrt{3} \\ \\ V = 24 \sqrt{3} ~cm^3$