Question

question 1. given circle o, if the radius co is 8 inches and the length of arc cd is 6π inches, what is the measure of central - angle ∠cod? enter your answer as a simplified fraction. use the keypad to enter your answer in the box. m∠cod = □ radians

Explanation:

Step1: Recall arc - length formula

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

Step2: Identify given values

We are given that $s = 6\pi$ inches and $r = 8$ inches.

Step3: Solve for the central angle $\theta$

From $s = r\theta$, we can express $\theta$ as $\theta=\frac{s}{r}$. Substituting $s = 6\pi$ and $r = 8$ into the formula, we get $\theta=\frac{6\pi}{8}=\frac{3\pi}{4}$ radians.

Answer:

$\frac{3\pi}{4}$