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 \(s\) of a circle is \(s = r\theta\), where \(r\) is the radius of the circle and \(\theta\) is the central angle in radians. First, convert the angle from degrees to radians. We know that \(\theta\) (in radians) \(=\frac{\pi}{180}\times\theta\) (in degrees). Given \(\theta = 45^{\circ}\), then \(\theta=\frac{\pi}{180}\times45=\frac{\pi}{4}\) radians. The radius \(r = 8\) cm.

Step2: Substitute values into the arc - length formula

Substitute \(r = 8\) and \(\theta=\frac{\pi}{4}\) into \(s=r\theta\). So \(s = 8\times\frac{\pi}{4}\).

Step3: Simplify the expression

\(s=\frac{8\pi}{4}=2\pi\)

Answer:

\(2\pi\)