Given that the radius of the circle is 6 cm.
The central angle is 120°
We need to determine the length of AB.
Length of AB:
The length of AB can be determined using the formula,
[tex]{arc \ length}=2 \pi r\left(\frac{\theta}{360}\right)[/tex]
Substituting [tex]\theta=120[/tex] and [tex]r=6[/tex] in the above formula, we get;
[tex]arc\ length}=2 \pi (6)\left(\frac{120}{360}\right)[/tex]
Simplifying the values, we get;
[tex]arc\ length}=2 \pi (6)\left(\frac{1}{3}\right)[/tex]
[tex]arc\ length}=12 \pi \left(\frac{1}{3}\right)[/tex]
[tex]arc\ length}=4 \pi[/tex]
Substituting π = 3.14, we have;
[tex]arc\ length}=4(3.14)[/tex]
[tex]arc\ length}=12.56[/tex]
Thus, the arc length of AB is 12.56 cm
