Question

question 8 of 10
the circumference of ⊙z is 84 cm. what is the length of (overparen{xy}) (the minor arc)?
a. 336 cm
b. 8.4 cm
c. 42 cm
d. 21 cm
e. 16 cm
f. 28 cm

Explanation:

Step1: Identify central - angle ratio

The central angle of the minor arc $\overset{\frown}{XY}$ is 90 degrees. Since a full - circle has 360 degrees, the ratio of the central angle of the minor arc $\overset{\frown}{XY}$ to the full - circle central angle is $\frac{90}{360}=\frac{1}{4}$.

Step2: Calculate arc length

The length of an arc is proportional to the central angle. Given the circumference $C = 84$ cm, and the ratio of the central angle of the arc to the full - circle central angle, the length of the minor arc $\overset{\frown}{XY}$ is $l=\frac{1}{4}\times C$. Substituting $C = 84$ cm, we get $l=\frac{1}{4}\times84 = 21$ cm.

Answer:

D. 21 cm