Step 1 :Given the diameter of the circle is 6 meters and the central angle is \( \frac{3 \pi}{5} \) radians.
Step 2 :First, calculate the radius of the circle. The radius is half of the diameter, so the radius is \( \frac{6}{2} = 3 \) meters.
Step 3 :Next, calculate the length of the arc. The formula for the length of an arc is \( s = r \theta \), where \( r \) is the radius and \( \theta \) is the angle in radians. Substituting the given values, we get \( s = 3 \times \frac{3 \pi}{5} \).
Step 4 :Finally, round the result to two decimal places. The length of the arc of the circle is \(\boxed{5.65}\) meters.