what is the length of the arc shown in red? the length of the arc is cm. (simplify your answer. type an…

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc 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 to convert degrees to radians, we use the conversion factor $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Given $\theta_{deg}=45^{\circ}$, then $\theta_{rad}=45\times\frac{\pi}{180}=\frac{\pi}{4}$ radians, and $r = 14$ cm.

Step2: Calculate the arc - length

Substitute $r = 14$ cm and $\theta=\frac{\pi}{4}$ into the arc - length formula $s=r\theta$. So, $s=14\times\frac{\pi}{4}=\frac{7\pi}{2}$ cm.

Answer:

$\frac{7\pi}{2}$