Question

1) (PUC) Um cubo tem área total igual a 84 m2. Sua diagonal mede:

Answer 1

Diagonal de um cubo de aresta

$\underline{\huge\mathsf{\ell}}$

$\huge\boxed{\boxed{\boxed{\boxed{\mathsf{D=\ell\sqrt{3}}}}}}$

Área total do cubo de aresta

$\underline{\huge\mathsf{\ell}}$  

 $\mathsf{A_{t}=6\cdot\ell^2}$

$\dotfill$

$\mathsf{A_{t}=6\cdot\ell^2}\\\mathsf{6\cdot\ell^2=84}\\\mathsf{\ell^2=\dfrac{84}{6}}\\\mathsf{\ell^2=14}\\\mathsf{\ell=\sqrt{14}~m}\\\mathsf{D=\ell\sqrt{3}}\\\mathsf{D=\sqrt{14}\cdot\sqrt{3}}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{D=\sqrt{42}~cm}}}}}$      

$\dotfill$

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