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 36.7 centimeters 15.7 centimeters 31.4 centimeters

Explanation:

Step1: Recall the arc - length formula

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

Step2: Substitute the given values

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

Step3: Calculate the value

\(s = 30\times\frac{\pi}{6}=5\pi\). Using \(\pi\approx3.14\), we get \(s\approx5\times3.14 = 15.7\) cm.

Answer:

15.7 centimeters