Question

The total surface area of a cube is 12,868cm^2. what is the length of one of the sides? what is the length of a diagonal that is not a diagonal of a face?

Answer 1

The surface area of a cube is given by:

$SA=6\cdot l^2$

where:

l = length of one of the sides

so:

$12868=6l^2$

solve for l:

$\begin{gathered} l=\sqrt[]{\frac{12868}{6}} \\ l\approx46.31 \end{gathered}$

The length of a diagonal that is not a diagonal of a face is:

$\begin{gathered} d=\sqrt[]{3}l \\ d\approx80.21 \end{gathered}$