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 arc length $s$ is $s = r\theta$, where $r$ is radius, $\theta$ is central angle in radians.

Step2: Substitute known values

We know $s = 9\pi$ and $\theta = \frac{3\pi}{4}$. Substitute into formula:
$9\pi = r \times \frac{3\pi}{4}$

Step3: Solve for $r$

Divide both sides by $\pi$, then multiply by $\frac{4}{3}$:
$9 = r \times \frac{3}{4}$
$r = 9 \times \frac{4}{3}$
$r = 12$

Answer:

12 inches