Calculate the Face Diagonal of a 2cm Cube: Geometric Measurement Problem

To solve this problem, we'll follow these steps:

• Step 1: Identify the side length of the square face on the cube.
• Step 2: Use the appropriate formula to find the diagonal of a square.
• Step 3: Calculate using the given measurements.

Now, let's work through these steps:
Step 1: The side length of the square face on the cube is given as 2 cm.
Step 2: The formula for the diagonal $d$ of a square with side length $s$ is $d = s\sqrt{2}$.
Step 3: Substituting the given side length into the formula, we get:

$d = 2 \times \sqrt{2}$

Therefore, the length of the diagonal of the cube's face is $2\sqrt{2}$ cm.

The correct multiple-choice answer that corresponds to our solution is:

• Choice 4: $2\times\sqrt{2}$ cm

Therefore, the solution to the problem is $2\sqrt{2}$ cm.