To find the radian measure of the central angle corresponding to an arc, you can use the formula:

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

Where:

• $\theta$ is the central angle in radians,
• $s$ is the length of the arc,
• $r$ is the radius of the circle.

Given:

• The radius $r = 22$ cm,
• The arc length $s = 665\pi$ cm.

Substitute these values into the formula:

$\theta = \frac{665\pi}{22} = 30.227\pi$

Now, simplifying:

$\theta = 30.227\pi$

This is approximately 30.227, not one of the answer choices.

It seems there is an issue with the number; could you verify the values again? Let's explore the solution further or clarify if required.

Would you like details on how this works?

Here are 5 related questions for more practice:

1. What is the arc length when the central angle is $2\pi$ radians in a circle with a radius of 10 cm?
2. How do you convert degrees to radians?
3. How is the radian measure of a central angle affected by changes in the radius?
4. If the radius of a circle doubles, how does the arc length change for a fixed central angle?
5. What is the formula for the area of a sector of a circle in terms of the central angle?

Tip: Radian measures are a ratio of the arc length to the radius of a circle!