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The problem involves calculating the arc length of a sector of a circle.

### Given:
- Radius of the circle, \( r = 6.5 \) cm
- Angle of the sector, \( \theta = 70^\circ \)

### Formula for Arc Length of a Sector:
The arc length \( L \) of a sector of a circle is given by the formula:
\[
L = \frac{\theta}{360^\circ} \times 2\pi r
\]

### Calculating the Arc Length:
Substitute the given values into the formula:

\[
L = \frac{70^\circ}{360^\circ} \times 2\pi \times 6.5 \, \text{cm}
\]

Let's compute this step-by-step.The arc length of the sector is approximately **7.94 cm**, correct to three significant figures.

Would you like more details on the steps involved, or do you have any other questions?

### Related Questions:
1. How do you calculate the area of a sector of a circle?
2. What is the difference between the arc length and the chord length?
3. How would the arc length change if the angle were doubled?
4. What happens to the arc length if the radius is increased?
5. How can you find the angle of a sector if you know the arc length and radius?

### Tip:
When working with sectors of a circle, always ensure that the angle is in degrees when using formulas involving \( \frac{\theta}{360^\circ} \). If using radians, the formula changes to \( \theta \times r \) for the arc length.

The diagram shows a sector of a circle with centre O. The radius of the circle is 6.5 cm. The acute angle AOB is 70°. Calculate the arc length of the sector, giving the answer correct to 3 significant figures.

This problem involves calculating the arc length of a sector with a radius of 6.5 cm and a central angle of 70°. Learn how to use the formula for arc length to solve the problem, including detailed steps. Suitable for students in Grades 8-10.

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