Question

find the exact length of the arc intercepted by the given central angle in the figure to the right.

Explanation:

Step1: Recall arc - length formula

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

Step2: Identify values of $r$ and $\theta$

From the figure, the radius $r = 14$ and the central - angle $\theta=\frac{\pi}{4}$.

Step3: Calculate the arc - length

Substitute $r = 14$ and $\theta=\frac{\pi}{4}$ into the formula $s = r\theta$. We get $s=14\times\frac{\pi}{4}=\frac{7\pi}{2}$.

Answer:

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