Question

question 23 of 44
what is the circumference of the circle shown below, given that the length of
$widehat{ab}$ (the minor arc) is 4?
image of a circle with center c, points a and b, and a 30° central angle
a. 40
b. 24
c. 48
d. 12

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc is $s = \frac{\theta}{360^\circ} \times C$, where $s$ is the arc length, $\theta$ is the central angle in degrees, and $C$ is the circumference of the circle.

Step2: Substitute known values

We know that $s = 4$ and $\theta = 30^\circ$. Substituting these into the formula: $4=\frac{30^\circ}{360^\circ}\times C$.

Step3: Solve for C

First, simplify $\frac{30^\circ}{360^\circ}=\frac{1}{12}$. So the equation becomes $4 = \frac{1}{12}C$. Multiply both sides by 12: $C = 4\times12 = 48$.

Answer:

C. 48