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

Answer:

The surface area of the cube is $128\ units^{2}$

Step-by-step explanation:

step 1

Find the length side of the cube

we know that

The diagonal of a cube is equal to

$d=b\sqrt{3}$

where

b is the length side of the cube

In this problem we have

$d=8\ units$

substitute and solve for b

$8=b\sqrt{3}$

$b=\frac{8}{\sqrt{3}}\ units$

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

$SA=6(\frac{8}{\sqrt{3}})^{2}=128\ units^{2}$