https://file.aiquickdraw.com/mathbot/file/1726382060174t5eid3wz.jpg

Let's work on solving the two problems in the image you provided:

### Problem 5:
Find the length of arc \( \overset{\frown}{AB} \) if the radius is 4 m and \( m\overset{\frown}{AB} = 180^\circ \).

- The formula for the length of an arc is:
  \[
  \text{Arc Length} = \frac{\theta}{360^\circ} \times 2\pi r
  \]
  Where:
  - \( \theta \) is the central angle (here \( 180^\circ \))
  - \( r \) is the radius (here \( 4 \, \text{m} \))
  
  Plugging in the values:
  \[
  \text{Arc Length} = \frac{180^\circ}{360^\circ} \times 2\pi \times 4
  = \frac{1}{2} \times 8\pi
  = 4\pi \, \text{m}
  \]
  So, the length of arc \( \overset{\frown}{AB} \) is:
  \[
  \text{Length of} \, \overset{\frown}{AB} = 4\pi \, \text{m} \approx 12.57 \, \text{m}
  \]

### Problem 6:
Find the area of sector \( COD \) if the radius is 10 cm and \( m\overset{\frown}{CD} = 45^\circ \).

- The formula for the area of a sector is:
  \[
  \text{Sector Area} = \frac{\theta}{360^\circ} \times \pi r^2
  \]
  Where:
  - \( \theta \) is the central angle (here \( 45^\circ \))
  - \( r \) is the radius (here \( 10 \, \text{cm} \))
  
  Plugging in the values:
  \[
  \text{Sector Area} = \frac{45^\circ}{360^\circ} \times \pi \times 10^2
  = \frac{1}{8} \times \pi \times 100
  = 12.5\pi \, \text{cm}^2
  \]
  So, the area of sector \( COD \) is:
  \[
  \text{Sector Area} = 12.5\pi \, \text{cm}^2 \approx 39.27 \, \text{cm}^2
  \]

Let me know if you'd like further explanation or details!

Here are 5 related questions to extend this topic:
1. How do you find the arc length if the central angle is given in radians?
2. What is the formula to find the perimeter of a sector?
3. How does the formula for arc length change if the central angle is measured in radians?
4. How do you calculate the area of a segment of a circle?
5. What is the relationship between arc length and the radius of the circle?

**Tip:** Always make sure that the angle used in the formula matches the unit (degrees or radians) of the formula being applied.

Find the length of AB if the radius is 4 m and mAB = 180°. Find the area of sector COD if the radius is 10 cm and mCD = 45°.

Learn how to calculate the length of an arc and the area of a sector in circle geometry. This problem uses the formulas for arc length and sector area, focusing on a radius of 4 meters and 10 cm, with angles of 180° and 45° respectively.

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