To find the length of the arc created by a central angle in a circle, we can use the formula:
\[ \text{Arc Length} = r \theta \]
where:
- \( r \) is the radius of the circle,
- \( \theta \) is the central angle in radians.
Given:
- Radius \( r = 6 \) cm,
- Central angle \( \theta = \frac{5\pi}{4} \) radians.
Now, substituting these values into the formula:
\[ \text{Arc Length} = 6 \cdot \frac{5\pi}{4} \]
Calculating this, we have:
\[ \text{Arc Length} = \frac{6 \cdot 5\pi}{4} = \frac{30\pi}{4} = \frac{15\pi}{2} \]
Thus, the length of the arc is:
\[ \frac{15\pi}{2} \text{ cm} \]
So, the final answer is:
\(\frac{15\pi}{2}\) cm.