Question

If the cube shown is 8 centimeters on all sides, what is the length of the diagonal, x, of the cube? (rounded to the nearest tenth)

Answer 1

Answer: 13.8 cm

Explanation:

Assuming the cube is the cube shown in the attached image, its diagonal is
`x`.

Now, for a cube which each side is
`a`, its diagonal is given by the pithagorean theorem:

`x=\sqrt{a^(2)+d^(2)}` (1)

Where
`d` is the hypothenuse of the right triangle formed in one of the cube's faces:

`d=√(3)a` (2)

Then the formula for the diagonal is:

`x=\sqrt{a^(2)+(√(3)a)^(2)}` (3)

`x=√(3)a` (4)

If
`a=8 cm`:

`x=√(3)8 cm` (5)

Finally:

x=13.8 cm