To find the length of an arc created by a central angle in a circle, you can use the formula:
\[ \text{Arc Length} = r \theta \]
where \( r \) is the radius of the circle and \( \theta \) is the central angle in radians.
In this case, the radius \( r \) is 6 cm and the central angle \( \theta \) is \( \frac{5\pi}{4} \) radians.
Now, plug in the values:
\[ \text{Arc Length} = 6 \times \frac{5\pi}{4} \]
Calculating this gives:
\[ \text{Arc Length} = \frac{30\pi}{4} = \frac{15\pi}{2} \]
Thus, the length of the arc is:
\[ \frac{15\pi}{2} \text{ cm} \]
If you need a numerical approximation, you can use \( \pi \approx 3.14 \):
\[ \frac{15 \times 3.14}{2} \approx 23.53 \text{ cm} \]
However, the exact answer for the arc length is
\[ \frac{15\pi}{2} \text{ cm} \]