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A circle has a radius of 22 centimeters. Arc XY has a length of 665⁢π centimeters. What is the radian measure of the corresponding central angle?
 
45⁢π
 
25⁢π
 
23⁢π
 

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.

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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!

A circle has a radius of 22 centimeters. Arc XY has a length of 665π centimeters. What is the radian measure of the corresponding central angle?

Explore how to calculate the radian measure of the central angle for an arc of length 665π centimeters in a circle with a radius of 22 centimeters. This geometry problem covers key concepts like arc length and radians, suitable for students in Grades 9-12.

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