Calculate Central Angle in Radians Given Sector Arc Length and Radius

Question

If the arc length of a sector is 3π cm and its radius is 12cm, then what is the central angle in radians?

Accepted Answer

$\frac{\pi}{4}$ radians

Answer

Step 1: Recall the formula for arc length of a sector: $l = r\theta$, where $l$ is arc length, $r$ is radius, and $\theta$ is the central angle in radians. Step 2: Substitute the given values $l=3\pi$ cm and $r=12$ cm into the formula: $3\pi = 12\theta$. Step 3: Solve for $\theta$: $\theta = \frac{3\pi}{12} = \frac{\pi}{4}$ radians.