Question

what is the length of the arc shown in red?
the length of the arc is □ cm.
(simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) is \(s=\frac{\theta}{360}\times2\pi r\), where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle.

Step2: Identify the values of \(\theta\) and \(r\)

From the problem, \(\theta = 60^{\circ}\) and \(r = 16\mathrm{cm}\).

Step3: Substitute the values into the formula

Substitute \(\theta = 60\) and \(r = 16\) into \(s=\frac{\theta}{360}\times2\pi r\).

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Answer:

\(\frac{16\pi}{3}\)