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Let's solve the given problem step by step.

### 1. **Circumference of the Circle**:
The formula for the circumference of a circle is:
\[
C = 2\pi r
\]
where \( r \) is the radius of the circle. Here, the radius is given as 8 meters.

\[
C = 2\pi \times 8 = 16\pi \approx 50.3 \, \text{meters}
\]
Thus, the circumference of the circle is approximately **50.3 meters**.

### 2. **Length of the Bolded Arc**:
The formula for the arc length is:
\[
\text{Arc Length} = \left( \frac{\text{measure}}{360} \right) \times 2\pi r
\]
Here, the central angle is \(270^\circ\) and the radius is \(8\) meters. Plugging in the values:

\[
\text{Arc Length} = \left( \frac{270}{360} \right) \times 2\pi \times 8
\]
\[
\text{Arc Length} = \left( \frac{3}{4} \right) \times 16\pi \approx 12\pi \approx 37.7 \, \text{meters}
\]
Thus, the arc length is approximately **37.7 meters**.

### 3. **Area of the Circle**:
The formula for the area of a circle is:
\[
\text{Area} = \pi r^2
\]
where \( r = 8 \) meters. Plugging in the values:

\[
\text{Area} = \pi \times 8^2 = 64\pi \approx 201.1 \, \text{square meters}
\]
Thus, the area of the circle is approximately **201.1 square meters**.

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Would you like more details on any of these steps? Feel free to ask!

Here are 5 related questions to further explore this topic:
1. How would the circumference change if the radius was doubled?
2. What is the formula for the area of a sector of a circle?
3. How do you calculate the area of a circle's segment (bounded by an arc and a chord)?
4. What is the relationship between the radius and the diameter of a circle?
5. How can you derive the formula for the circumference of a circle?

**Tip**: Remember that the circumference and area both depend on the square of the radius—so doubling the radius increases the area four times!

Find the circumference, arc length, and area for a circle with a radius of 8 meters and a 270° central angle.

Learn how to calculate the circumference, arc length, and area of a circle with a radius of 8 meters and a 270° central angle. This problem covers key geometry concepts, including circle properties, arc length formula, and area calculation. Suitable for students in Grades 8-10.

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