Question

sat #1
math - part 1
the circle shown has center o and a radius of 3 inches. if angle aob measures 120°, what is the length of arc ab, in inches?
a π
b 2π
c 3π
d 6π

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) of a circle is \(s = r\theta\), where \(r\) is the radius of the circle and \(\theta\) is the central angle in radians. First, convert the angle from degrees to radians. We know that \(\theta\) (in radians) \(=\frac{\pi}{180}\times\theta\) (in degrees). Given \(\theta = 120^{\circ}\), then \(\theta=\frac{\pi}{180}\times120=\frac{2\pi}{3}\) radians, and \(r = 3\) inches.

Step2: Substitute values into the arc - length formula

Substitute \(r = 3\) and \(\theta=\frac{2\pi}{3}\) into \(s=r\theta\). So \(s=3\times\frac{2\pi}{3}\).

Answer:

\(2\pi\), so the answer is B.