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. \\(\bigcirc\\) 6 inches \\(\bigcirc\\) 12 inches \\(\bigcirc\\) 18 inches \\(\bigcirc\\) 24 inches

Explanation:

Step1: Recall arc length formula

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

Step2: Substitute known values

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

Step3: Solve for $r$

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

Answer:

B. 12 inches