https://file.aiquickdraw.com/mathbot/file/1726913435309uv18a0qv.jpg

The problem involves finding the area of the shaded region, which represents an annulus or ring formed between two concentric circles. To calculate the area of the shaded region, we need to follow these steps:

### Formula:
The area of the shaded region (annulus) is the difference between the area of the larger circle and the smaller circle:
\[
A_{\text{shaded}} = A_{\text{larger}} - A_{\text{smaller}}
\]
Where the area of a circle is given by:
\[
A = \pi \times r^2
\]
### Step-by-step Solution:
1. **Identify the radii of the circles:**
   - The radius of the larger circle is \( R = 5 \, \text{m} \).
   - The radius of the smaller circle is \( r = 4 \, \text{m} \).

2. **Calculate the area of the larger circle:**
   \[
   A_{\text{larger}} = \pi \times 5^2 = 25\pi \, \text{m}^2
   \]

3. **Calculate the area of the smaller circle:**
   \[
   A_{\text{smaller}} = \pi \times 4^2 = 16\pi \, \text{m}^2
   \]

4. **Calculate the area of the shaded region:**
   \[
   A_{\text{shaded}} = 25\pi - 16\pi = 9\pi \, \text{m}^2
   \]

5. **Final Answer (to 1 decimal place):**
   \[
   A_{\text{shaded}} = 9 \times 3.1416 = 28.27 \, \text{m}^2
   \]
   Rounding to 1 decimal place: 
   \[
   A_{\text{shaded}} \approx 28.3 \, \text{m}^2
   \]

The shaded area is **28.3 m²**.

Would you like any further details or have questions? Here are five related questions to explore:

1. What is the formula for the area of a circle?
2. How would the solution change if the radii were given in centimeters?
3. How do you convert square meters to square centimeters?
4. Can you calculate the circumference of the larger circle?
5. What is the percentage of the smaller circle's area relative to the larger circle?

**Tip:** When working with areas of circles, always square the radius before multiplying by π to avoid common calculation mistakes.

The diagram contains two circles, both centered on O. The radius of the larger circle is 5 m, and the radius of the smaller circle is 4 m. Calculate the shaded area, which is the region between the two circles. Give your answer to 1 decimal place.

Learn how to calculate the area of the shaded region between two concentric circles with radii 5m and 4m. Using the formula for the area of a circle (A = π × r²), this step-by-step solution is ideal for middle school students in Grades 6-8.

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