Question

One diagonal of a cube has length 12. Compute the surface area of the cube.

Answer 1

Answer:

The surface area of the cube is $288\ units^{2}$

Step-by-step explanation:

we know that

The length of a diagonal of a cube is equal to

$D=b\sqrt{3}$

where

b is the length side of a cube

In this problem we have

$D=12\ units$

so

$12=b\sqrt{3}$

solve for b

$b=\frac{12}{\sqrt{3}}\ units$

Simplify

$b=4\sqrt{3}\ units$

Find the surface area of the cube

The surface area of the cube is equal to

$SA=6b^{2}$

substitute the value of b

$SA=6(4\sqrt{3})^{2}=288\ units^{2}$