Question

A diagonal de um cubo mede 3 cm. Calcule o volume desse cubo.
(mostrar o desenvolvimento se possível)

Answer 1

$\boxed{D=a \sqrt{3}\ e\ V=a^3}\\\\\\D=a \sqrt{3} \\3=a \sqrt{3}\\\\a= \frac{3}{ \sqrt{3} } \cdot \frac{ \sqrt{3} }{ \sqrt{3} } \\\\a= \frac{3 \sqrt{3} }{3} \\\\\boxed{a= \sqrt{3} }\\\\\\ V=a^3\\V=( \sqrt{3} )^3\\V= \sqrt{3^3}\\V= \sqrt{81}\\\\\boxed{\boxed{V=9\ cm^3 }}$