Question

consider circle n with radius 30 cm and $\theta = \frac{pi}{6}$ radians. what is the approximate length of minor arc lm? round to the nearest tenth of a centimeter.○ 12.4 centimeters○ 15.7 centimeters○ 31.4 centimeters○ 36.7 centimeters

Explanation:

Step1: Recall arc length formula

The formula for arc length \(s\) when the central angle \(\theta\) is in radians is \(s = r\theta\), where \(r\) is the radius of the circle.

Step2: Substitute given values

Substitute \(r = 30\) cm and \(\theta = \frac{\pi}{6}\) radians into the formula:
\(s = 30 \times \frac{\pi}{6}\)

Step3: Calculate and approximate

Simplify the expression:
\(s = 5\pi \approx 5 \times 3.1416 = 15.708\)
Round to the nearest tenth.

Answer:

15.7 centimeters