Answer:
The surface area of the cube is [tex]128\ units^{2}[/tex]
Step-by-step explanation:
step 1
Find the length side of the cube
we know that
The diagonal of a cube is equal to
[tex]d=b\sqrt{3}[/tex]
where
b is the length side of the cube
In this problem we have
[tex]d=8\ units[/tex]
substitute and solve for b
[tex]8=b\sqrt{3}[/tex]
[tex]b=\frac{8}{\sqrt{3}}\ units[/tex]
step 2
Find the surface area of the cube
The surface area of the cube is equal to
[tex]SA=6b^{2}[/tex]
substitute the value of b
[tex]SA=6(\frac{8}{\sqrt{3}})^{2}=128\ units^{2}[/tex]
