Question

question 8 of 10
the length of \\(\overarc{xy}\\) (the minor arc) is 48 cm. what is the circumference of \\(\odot z\\)?
image of a circle with center z, points x and y on the circumference, and angle ∠xzy = 60°
a. 288 cm
b. 192 cm
c. 326 cm
d. 301.44 cm
e. 24 cm
f. 384 cm

Explanation:

Step1: Find arc length ratio

Arc length = $\frac{\theta}{360^\circ} \times$ circumference. $\theta=60^\circ$, ratio = $\frac{60}{360}=\frac{1}{6}$.

Step2: Calculate circumference

Let $C$ = circumference. $\frac{1}{6}C=48$, so $C=48\times6=288$.

Answer:

A. 288 cm