What is the central angle (in radians) of a sector with arc length 12 cm in a circle of radius 4 cm?

Correct Answer: 3 radians

Step-by-Step Explanation:

1. Understand the Formula:

The relationship between the arc length of a sector ($s$), the radius of the circle ($r$), and the central angle in radians ($\theta$) is given by the formula:

$s=r·\theta$

2. Identify the Given Values:

From the question, we are given:

Arc length, $s=12\text{cm}$

Radius, $r=4\text{cm}$

3. Rearrange the Formula to Solve for the Central Angle ($\theta$):

Rearranging $s=r·\theta$ to isolate $\theta$ gives:

$\theta =\frac{s}{r}$

4. Calculate the Central Angle:

Substitute the given values into the formula:

$\theta =\frac{12}{4}$

$\theta =3\text{radians}$

Thus, the central angle of the sector is 3 radians.