https://file.aiquickdraw.com/mathbot/file/17255327312915u278ih5.jpg

To solve this problem, we need to calculate the shaded area of the circle. The diagram shows a quarter of a circle shaded, and we are given that the radius of the circle is 3 meters. Let's go through the steps to calculate the shaded area.

### Step 1: Find the Area of the Full Circle
The formula for the area of a circle is:
\[
A = \pi r^2
\]
where \( r \) is the radius of the circle.

Given:
- \( r = 3 \) meters

Thus, the area of the full circle is:
\[
A_{\text{full}} = \pi \times 3^2 = 9\pi \text{ square meters}
\]

### Step 2: Calculate the Area of the Quarter Circle (Shaded Area)
Since the shaded area is a quarter of the circle, the area of the shaded region is:
\[
A_{\text{shaded}} = \frac{1}{4} \times 9\pi = \frac{9\pi}{4} \text{ square meters}
\]

### Step 3: Approximate the Shaded Area
We will approximate \( \pi \) as \( 3.14 \) for practical purposes. Therefore, the shaded area is approximately:
\[
A_{\text{shaded}} \approx \frac{9 \times 3.14}{4} = \frac{28.26}{4} \approx 7.065 \text{ square meters}
\]

### Step 4: Choose the Closest Answer
From the options provided:
- (A) \( 7\frac{1}{4} \, \text{m}^2 \)
- (B) \( 14\frac{1}{4} \, \text{m}^2 \)
- (C) \( 21\frac{1}{2} \, \text{m}^2 \)
- (D) \( 28\frac{3}{4} \, \text{m}^2 \)

The closest answer to 7.065 square meters is **(A) \( 7\frac{1}{4} \, \text{m}^2 \)**.

### Conclusion
The shaded area is closest to \( 7\frac{1}{4} \, \text{m}^2 \), which corresponds to answer **(A)**.

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Would you like more details or have any further questions?

Here are 5 related questions for further practice:
1. How would the shaded area change if the radius were doubled?
2. What is the perimeter of the quarter circle?
3. How would you calculate the area of the shaded region if it were a semicircle instead?
4. What would the shaded area be if only one-eighth of the circle were shaded?
5. How does the area of the quarter circle compare to that of a square inscribed in the circle?

**Tip:** Always check if the area given in the question is for a full shape or just a portion, and adjust your calculations accordingly.

The radius of the circle is 3 m. The shaded area would be closest to:

Learn how to find the shaded area of a quarter circle with a radius of 3 m. This problem involves calculating the area of a circle and using fractions to determine the portion of the shaded region. Suitable for students in Grades 6-8.

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