Question

consider circle c with angle acb measuring $\frac{3pi}{4}$ radians. if minor arc ab measures $9pi$ inches, what is the length of the radius of circle c? if necessary, round your answer to the nearest inch. 6 inches 12 inches 18 inches 24 inches

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: Substitute given values

We are given that $s = 9\pi$ inches and $\theta=\frac{3\pi}{4}$ radians. Substituting these values into the formula $s = r\theta$, we get $9\pi=r\times\frac{3\pi}{4}$.

Step3: Solve for $r$

To solve for $r$, we can first multiply both sides of the equation $9\pi=r\times\frac{3\pi}{4}$ by $\frac{4}{3\pi}$.
\[

$$\begin{align*} r&=\frac{9\pi\times4}{3\pi}\\ &=\frac{36\pi}{3\pi}\\ & = 12 \end{align*}$$

\]

Answer:

12 inches