Answer:
D. 31.4cm
Step-by-step explanation:
To know the measure of the arc AB, we must first know the measure of the perimeter (the circumference) of the circle:
[tex]c=2\pi r[/tex]
where [tex]\pi[/tex] is a constant, [tex]\pi=3.1416[/tex]
and [tex]r[/tex] is the radius which is the line that goes from the center of the circle to a point on the circumference, in this case:
[tex]r=30cm[/tex]
so the measurement of the circumference is:
[tex]c=2(3.1416)(30cm)\\c=188.5cm[/tex]
Now, we don't want the measurement of the entire circumference, we only want 60 ° of the total 360 ° degrees of the circle. For this we must divide the measure that we find for the circumference by 360 and multiply the result by 60:
[tex]AB=\frac{188.5cm}{360}(60)\\ \\AB=(0.5236cm)(60)\\AB=31.4cm[/tex]which is option D
