Question

calcule a medida da diagonal, a área total e o volume de um cubo cuja soma das medidas das arestas é igual a 48 cm

Answer 1

$\large\boxed{\begin{array}{l}\sf seja~\ell~a~aresta~do~cubo.\\\sf como~o~cubo~possui~12~arestas~e\\\sf a~soma~de~todas~elas~\acute e~48,\\\sf podemos~escrever:\\\sf 12\ell=48\\\sf \ell=\dfrac{48}{12}\\\\\sf \ell=4~cm\\\underline{\rm Diagonal~do~cubo:}\\\sf d=\ell\sqrt{3}\\\sf d=4\sqrt{3}~cm\\\underline{\rm \acute Area~total:}\\\sf A_t=6\cdot\ell^2\\\sf A_t=6\cdot4^2\\\sf A_t=6\cdot16\\\sf A_t=96~cm^2\\\underline{\rm Volume~do~cubo:}\\\sf V=\ell^3\\\sf V=4^3\\\sf V=64~cm^3\end{array}}$