Question

question 21 of 44
if the circumference of the circle below is 72, what is the length of (overarc{xy}) (the minor arc)?
image of a circle with center z, points x and y, and a central angle of (40^circ) between zx and zy
(\bigcirc) a. 36
(\bigcirc) b. 72
(\bigcirc) c. 8
(\bigcirc) d. 18

Explanation:

Step1: Recall arc length formula

The length of an arc \( s \) is given by \( s=\frac{\theta}{360^\circ}\times C \), where \( \theta \) is the central angle in degrees and \( C \) is the circumference of the circle.

Step2: Identify values

Here, \( \theta = 40^\circ \) and \( C = 72 \).

Step3: Substitute into formula

Substitute the values into the formula: \( s=\frac{40^\circ}{360^\circ}\times72 \).
Simplify \( \frac{40}{360}=\frac{1}{9} \), then \( s = \frac{1}{9}\times72 = 8 \).

Answer:

C. 8