Question

the circumference of the circle shown below is 54 centimeters. which expression gives the length in centimeters of \\(\overarc{xy}\\)? \\(\bigcirc\\) a. \\(\frac{360}{120}\bullet54\\) \\(\bigcirc\\) b. \\(\frac{120}{360}\bullet54\\) \\(\bigcirc\\) c. \\(\frac{120}{360}\bullet54\pi\\) \\(\bigcirc\\) d. \\(\frac{360}{120}\bullet54\pi\\)

Explanation:

Step1: Recall arc length formula

Arc length = $\frac{\text{central angle}}{360^\circ} \times \text{circumference}$

Step2: Substitute given values

Central angle = $120^\circ$, circumference = 54 cm
Expression: $\frac{120}{360} \cdot 54$

Answer:

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