Sector Arc Length Calculation

To find the length of the arc of a sector, we use the formula:

Arc Length, $L = \frac{\theta}{360°} \times 2\pi r$

Where:

• $\theta$ is the angle of the sector in degrees.
• $r$ is the radius of the sector.
• $\pi$ is the mathematical constant Pi (approximately $\frac{22}{7}$).

Applying the Formula

Given:

• Angle, $\theta = 30°$
• Radius, $r = 42$ cm

Substitute the values into the formula:

$L = \frac{30°}{360°} \times 2 \times \frac{22}{7} \times 42 \text{ cm}$

Step-by-Step Calculation

1. Simplify the fraction of the angle:

   $\frac{30°}{360°} = \frac{1}{12}$

2. Substitute the simplified fraction back into the formula:

   $L = \frac{1}{12} \times 2 \times \frac{22}{7} \times 42 \text{ cm}$

3. Perform the multiplication:

   $L = \frac{1}{12} \times 2 \times 22 \times \frac{42}{7} \text{ cm}$

   $L = \frac{1}{12} \times 2 \times 22 \times 6 \text{ cm}$

4. Further simplify:

   $L = \frac{1}{12} \times 264 \text{ cm}$

5. Final result:

   $L = 22 \text{ cm}$

Therefore, the length of the arc of the sector is 22 cm.