To determine the length of the arc of a sector given its radius and central angle, follow these steps:
1. Convert the central angle from degrees to radians:
- The central angle is given as \( 30^\circ \).
- The formula to convert degrees to radians is:
[tex]\[
\text{Radians} = \left( \frac{\text{Degrees} \times \pi}{180} \right)
\][/tex]
Plugging in the value:
[tex]\[
\text{Central angle in radians} = \left( \frac{30 \times \pi}{180} \right) = \frac{\pi}{6} \approx 0.524
\][/tex]
2. Calculate the arc length:
- The formula for the arc length \( s \) of a sector is:
[tex]\[
s = r \theta
\][/tex]
where \( r \) is the radius and \( \theta \) is the central angle in radians.
Plugging in the values:
[tex]\[
s = 10 \times \frac{\pi}{6} = \frac{10 \pi}{6} = \frac{5 \pi}{3} \approx 5.236
\][/tex]
Given this calculation, the length of the arc of the sector is \( \frac{5 \pi}{3} \) inches.
Hence, the correct choice is:
[tex]\[
(1) \frac{5 \pi}{3}
\][/tex]
