A cube has an edge length that is a rational number of centimeters. Identify which measurement will require the use of irrational numbers? (1 point)

To determine which measurement will require the use of irrational numbers for a cube with a rational edge length, let's analyze each option:

1. **The diagonal of one of the cube's faces**: The diagonal \(d\) of a face of a cube with edge length \(a\) can be calculated using the Pythagorean theorem:
\[
d = \sqrt{a^2 + a^2} = \sqrt{2a^2} = a\sqrt{2}
\]
Since \(a\) is rational, \(a\sqrt{2}\) will be irrational because \(\sqrt{2}\) is an irrational number.

2. **The volume of the cube**: The volume \(V\) of a cube with edge length \(a\) is given by:
\[
V = a^3
\]
Since \(a\) is rational, \(a^3\) is also rational.

3. **The surface area of the cube**: The surface area \(S\) of a cube is calculated as:
\[
S = 6a^2
\]
Since \(a\) is rational, \(6a^2\) is also rational.

4. **The area of one of the cube's faces**: The area \(A\) of one face is:
\[
A = a^2
\]
Since \(a\) is rational, \(a^2\) is also rational.

Based on this analysis, the only measurement that requires the use of irrational numbers is:

**The diagonal of one of the cube's faces**.