Both circles have the same center. What is the area of the shaded region?
d=24 m
11 m

To solve the problem of finding the area of the shaded region between two concentric circles (circles with the same center), we need to follow these steps:

1. **Identify the given values**:
   - The diameter of the larger circle (\(d\)) is 24 meters.
   - The radius of the smaller circle (\(r\)) is 11 meters.

2. **Calculate the radius of the larger circle**:
   - The radius of the larger circle (\(R\)) is half of the diameter.
   \[
   R = \frac{d}{2} = \frac{24}{2} = 12 \text{ meters}
   \]

3. **Find the area of the larger circle**:
   - The area of a circle is given by the formula \(A = \pi R^2\).
   \[
   A_{\text{large}} = \pi (12)^2 = 144\pi \text{ square meters}
   \]

4. **Find the area of the smaller circle**:
   - Similarly, the area of the smaller circle is:
   \[
   A_{\text{small}} = \pi (11)^2 = 121\pi \text{ square meters}
   \]

5. **Calculate the area of the shaded region**:
   - The area of the shaded region is the difference between the area of the larger circle and the smaller circle.
   \[
   A_{\text{shaded}} = A_{\text{large}} - A_{\text{small}} = 144\pi - 121\pi = 23\pi \text{ square meters}
   \]

So, the area of the shaded region is \(23\pi\) square meters, which is approximately \(72.26\) square meters if you use \(\pi \approx 3.14\).

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How does the area of the shaded region change if the radius of the smaller circle is increased by 1 meter?
2. What would the area of the shaded region be if the diameter of the larger circle were doubled?
3. How would you calculate the circumference of each circle?
4. What if the circles had different centers? How would that affect the area of the shaded region?
5. How would you calculate the area of the shaded region if the smaller circle were an ellipse?

**Tip:** When working with concentric circles, remember that the area of the shaded region can be found by simply subtracting the area of the smaller circle from the area of the larger circle.

Learn how to calculate the area of the shaded region between two concentric circles with different radii. This problem involves geometry concepts, specifically circle geometry, and utilizes the formula for the area of a circle. Suitable for students in Grades 7-9.

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