Calculate the Face Diagonal of a 3-Centimeter Cube: Finding Corner-to-Corner Distance

Question

Given below is a cube that has edges measuring 3 cm.

What is the length of the diagonal of the face?

00:00 Find the length of the face diagonal in a cube

00:03 The edge length according to the given data

00:08 In a cube, all edges are equal

00:11 A face in a cube is a square, therefore all angles are right angles

00:14 Therefore, we'll use the Pythagorean theorem in triangle ABD

00:20 We'll substitute appropriate values according to the data and solve for DB

00:47 Extract the root

00:51 Factor 18 into 9 and 2

01:01 And this is the solution to the question

To find the length of the diagonal of a face of a cube with edges measuring 3 cm, we should consider the geometry of the face, which is a square.

The length of the diagonal $d$ of a square with side length $s$ is found using the Pythagorean theorem, which gives us:

\text{Diagonal of the face} = s\sqrt{2}

Substituting the given value $s = 3$ cm, we have:

d = 3\sqrt{2}

Therefore, the length of the diagonal of the face is $3\sqrt{2}$ .

$3\sqrt{2}$