Question

finding arc length given a central angle measure. in circle o, central angle aob measures (\frac{2}{3}) radians. what is the length of arc ab? 18 cm

Explanation:

Step1: Recall 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.

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

From the problem, the radius of the circle $r = 18$ cm and the central angle $\theta=\frac{2\pi}{3}$ radians.

Step3: Calculate the arc - length

Substitute $r = 18$ and $\theta=\frac{2\pi}{3}$ into the formula $s = r\theta$. So $s=18\times\frac{2\pi}{3}$.
\[

$$\begin{align*} s&=\frac{18\times2\pi}{3}\\ & = 12\pi\text{ cm} \end{align*}$$

\]

Answer:

$12\pi$ cm