The formula for the length of an arc $L$ of a circle is:

$L = r \theta$

where:

• $L$ is the arc length,
• $r$ is the radius of the circle,
• $\theta$ is the angle subtended by the arc (in radians).

Given:

• $L = 6 \pi \, \text{cm}$,
• $r = 7 \, \text{cm}$.

We need to find $\theta$, so rearranging the formula for $\theta$:

$\theta = \frac{L}{r}$

Substituting the known values:

$\theta = \frac{6 \pi}{7}$

Let's compute that value and round it to two decimal places.

$\theta \approx 2.69 \, \text{radians}$

So, the angle associated with this arc is approximately $\boxed{2.69}$ radians.

Would you like more details or have any questions? Here are five related questions for further exploration:

1. How do you convert this angle in radians to degrees?
2. What would be the arc length if the angle was $\pi/2$ radians?
3. If the radius were doubled, how would the arc length change?
4. How is the circumference of the circle related to the arc length?
5. Can you find the sector area associated with this arc?

Tip: Always remember that $2\pi$ radians corresponds to a full circle (360 degrees).