Question

the circumference of the circle shown below is 54 centimeters. which expression gives the length in centimeters of (overarc{xy})?
a. (\frac{360}{120} \bullet 54)
b. (\frac{120}{360} \bullet 54pi)
c. (\frac{120}{360} \bullet 54)
d. (\frac{360}{120} \bullet 54pi)

Explanation:

Step1: Recall arc length formula

The length of an arc is a fraction of the circumference. The fraction is $\frac{\text{central angle}}{360^\circ}$, so arc length $=\frac{\theta}{360^\circ}\times$ circumference.

Step2: Identify values

Here, central angle $\theta = 120^\circ$, circumference $= 54$ cm.

Step3: Substitute into formula

Arc length $\overarc{XY}=\frac{120}{360}\times54$, which matches option C.

Answer:

C. $\frac{120}{360}\bullet54$