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Let's analyze and solve the problem step by step.

The function for the radius \( r(C) \) of a circle in terms of its circumference \( C \) is given by:
\[
r(C) = \frac{C}{2\pi}
\]

### Part (b): Find \( r(24\pi) \) and interpret its meaning.

To find \( r(24\pi) \), substitute \( C = 24\pi \) into the function:

\[
r(24\pi) = \frac{24\pi}{2\pi}
\]

Now, simplify this expression:
\[
r(24\pi) = \frac{24\pi}{2\pi} = \frac{24}{2} = 12
\]

### Interpretation

The result \( r(24\pi) = 12 \) means that a circle with a circumference of \( 24\pi \) has a radius of 12 units.

The correct interpretation choice is:
- **"The radius of a circle with a circumference of \( 24\pi \) is \( r(24\pi) \)."**

Would you like further details on this solution, or do you have any questions?

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Here are some related questions for further exploration:

1. How would the radius change if the circumference were \( 48\pi \) instead of \( 24\pi \)?
2. What is the formula for the area of a circle in terms of its circumference?
3. How would you solve for \( C \) in terms of \( r \) if \( r(C) = \frac{C}{2\pi} \)?
4. What would the radius be for a circle with a circumference of \( 10\pi \)?
5. How does the formula \( r(C) = \frac{C}{2\pi} \) relate to the formula \( C = 2\pi r \)?

### Tip:
When working with formulas, substituting values carefully and simplifying step-by-step can prevent errors and ensure clarity.

Given r(C) = C / (2 * pi), find r(24pi) and interpret its meaning.

Learn how to find the radius of a circle with a given circumference of 24π using the formula r(C) = C / (2 * pi). This problem illustrates the relationship between circumference and radius, suitable for students in Grades 8-10.

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