https://file.aiquickdraw.com/mathbot/file/1729061656935cu5mifqg.jpg

The image shows a sector of a circle with a central angle of 80° and a radius of 10 meters. To analyze the sector, we can calculate different aspects of it, such as:

1. **Arc Length**: The arc length \( L \) of a sector is given by the formula:
   \[
   L = 2\pi r \times \frac{\theta}{360}
   \]
   where \( r \) is the radius, and \( \theta \) is the central angle in degrees.

2. **Area of the Sector**: The area \( A \) of a sector is calculated by:
   \[
   A = \pi r^2 \times \frac{\theta}{360}
   \]
   where \( r \) is the radius, and \( \theta \) is the central angle.

Let's calculate both the arc length and the area of the sector.

1. **Arc Length**:
   \[
   L = 2\pi (10) \times \frac{80}{360} = 20\pi \times \frac{80}{360} = 20\pi \times \frac{2}{9} = \frac{40\pi}{9} \approx 13.96 \, \text{meters}
   \]

2. **Area of the Sector**:
   \[
   A = \pi (10)^2 \times \frac{80}{360} = 100\pi \times \frac{80}{360} = 100\pi \times \frac{2}{9} = \frac{200\pi}{9} \approx 69.81 \, \text{square meters}
   \]

So, the **arc length** is approximately \( 13.96 \, \text{m} \) and the **area** of the sector is approximately \( 69.81 \, \text{m}^2 \).

Do you need more details or have any questions?

Here are 5 questions based on this problem:
1. How would the area change if the central angle were increased to 90°?
2. What would the arc length be if the radius were doubled but the angle stayed the same?
3. How can the formula for the arc length be derived from the circumference of a circle?
4. What would the area of the entire circle be, based on the radius given?
5. How is the proportion \( \frac{\theta}{360} \) related to the full circle in these calculations?

**Tip:** When working with sectors, always express the angle in degrees or radians according to the formula you're using, and convert if necessary!

What is the arc length and area of a sector with a radius of 10 meters and a central angle of 80°?

Learn how to calculate the arc length and area of a sector with a radius of 10 meters and a central angle of 80°. This step-by-step guide includes geometry formulas and a practical example for students in Grades 8-10.

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