Question

for the problem below, \\( \theta \\) is a central angle in a circle of radius \\( r \\). find the length of arc \\( s \\) cut off by \\( \theta \\). answer exactly; do not round. \\( \theta=\frac{\pi}{3} \\) radians; \\( r=18 \\) centimeters \\( s= \\) centimeters

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) 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 into the formula

Given \(r = 18\) centimeters and \(\theta=\frac{\pi}{3}\) radians. Substitute these values into the formula \(s = r\theta\):

$$
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$$

Step3: Simplify the expression

$$
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$$

Answer:

\(6\pi\)