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

A face diagonal connects two opposite corners on the same square face, while a space diagonal connects opposite corners of the entire cube through its interior. Face diagonal uses $s\sqrt{2}$, space diagonal uses $s\sqrt{3}$.

The face of a cube is a square, and the diagonal creates a right triangle with two sides of length 3 cm. Using $a^2 + b^2 = c^2$, we get $3^2 + 3^2 = d^2$.

Understanding is better than memorizing! The formula comes from applying the Pythagorean theorem to a square. If you understand why it works, you'll never forget it and can derive it yourself.

Factor out perfect squares: $\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$. Always look for the largest perfect square factor to simplify radicals.

The same method applies! For any cube with edge length s, the face diagonal is always $s\sqrt{2}$. Just substitute your value for s.