The image shows a sector of a circle with the following information:

• The radius of the circle is 6 cm.
• The arc length is 62 cm.
• The central angle at point A is represented but not explicitly given.

We can solve for the central angle using the formula for the arc length of a circle:

$L = r \cdot \theta$

Where:

• $L$ is the arc length (62 cm),
• $r$ is the radius of the circle (6 cm),
• $\theta$ is the central angle in radians.

Step 1: Solve for the central angle ($\theta$)

$\theta = \frac{L}{r} = \frac{62}{6} \approx 10.33 \text{ radians}$

This central angle is approximately $10.33$ radians.

Would you like more details or clarification on this calculation?

Here are 5 related questions to explore:

1. How do you convert a radian measure to degrees?
2. What is the area of the sector formed by this central angle?
3. How is the circumference of the entire circle calculated?
4. What would the central angle be if the arc length were 50 cm?
5. How does the length of the arc depend on the radius and central angle?

Tip: Radians are often more useful in mathematical contexts because they simplify formulas for circles and periodic functions.