Question

The diagonal of a cube is a segment whose endpoints are vertices that are not on the same face. Find the surface area of a cube with diagonal length 8 units. Round your answer to three decimal places

Answer 1

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

Explanation:

step 1

Find the length side of the cube

we know that

The diagonal of a cube is equal to

`d=b√(3)`

where

b is the length side of the cube

In this problem we have

`d=8\ units`

substitute and solve for b

`8=b√(3)`

`b=(8)/(√(3))\ units`

step 2

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((8)/(√(3)))^(2)=128\ units^(2)`