Question

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

Answer 1

The surface area of the cube is
`288\ units^(2)`

Explanation:

we know that

The length of a diagonal of a cube is equal to

`D=b√(3)`

where

b is the length side of a cube

In this problem we have

`D=12\ units`

so

`12=b√(3)`

solve for b

`b=(12)/(√(3))\ units`

Simplify

`b=4√(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√(3))^(2)=288\ units^(2)`