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)

Question

asked Jul 28, 2021 192k views

1 Answer

Kevin Pang · Answer 1 · 2021-08-02T09:59:10+0000

Answer: 13.8 cm

Explanation:

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

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

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

Where
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