Question

a circle has a circumference of 12cm. the measure of a central angle of the circle is 60 degrees. what is the length of the arc associated with this angle?
1 cm
6 cm
4 cm
2 cm

Explanation:

Step1: Recall arc length formula

The length of an arc is a fraction of the circumference. The fraction is the ratio of the central angle to the total angle in a circle (360 degrees). So, arc length \( L=\frac{\theta}{360^\circ}\times C \), where \( \theta \) is the central angle and \( C \) is the circumference.

Step2: Substitute values

Given \( \theta = 60^\circ \) and \( C = 12 \) cm. Substitute into the formula: \( L=\frac{60^\circ}{360^\circ}\times12 \).

Step3: Simplify the expression

Simplify \( \frac{60}{360}=\frac{1}{6} \), then \( L=\frac{1}{6}\times12 = 2 \) cm? Wait, no, wait: Wait, \( \frac{60}{360}=\frac{1}{6} \)? Wait 60/360 is 1/6? Wait 606=360, so yes. Then 1/6 of 12 is 2? But wait, maybe I made a mistake. Wait, 60 degrees is 1/6 of 360? Wait 360/60=6, so 60 degrees is 1/6 of the circle? Wait no, 360 divided by 60 is 6, so 60 degrees is 1/6 of the circle? Wait, no: 606=360, so 60 degrees is 1/6 of 360? Wait, 1/6 of 360 is 60, yes. So the arc length is 1/6 of the circumference. Wait 12(1/6)=2. But the options include 2 cm. Wait, but let me check again. Wait, maybe I messed up the fraction. Wait, 60 degrees over 360 degrees is 60/360 = 1/6. So arc length is (1/6)12 = 2. So the answer is 2 cm.

Answer:

2 cm (corresponding to the option with "2 cm")