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
- Simplify the fraction of the angle:
$\frac{30°}{360°} = \frac{1}{12}$
- Substitute the simplified fraction back into the formula:
$L = \frac{1}{12} \times 2 \times \frac{22}{7} \times 42 \text{ cm}$
- Perform the multiplication:
$L = \frac{1}{12} \times 2 \times 22 \times \frac{42}{7} \text{ cm}$
$L = \frac{1}{12} \times 2 \times 22 \times 6 \text{ cm}$
- Further simplify:
$L = \frac{1}{12} \times 264 \text{ cm}$
- Final result:
$L = 22 \text{ cm}$
Therefore, the length of the arc of the sector is 22 cm.
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