Question

1. what is the major arc length of a circle with a radius of 10 units and a central angle of 150 degrees?

a. $\frac{15pi}{2}$ units
b. $\frac{20pi}{3}$ units
c. $\frac{31pi}{3}$ units
d. $\frac{25pi}{3}$ units

Explanation:

Answer:

First, find the minor - arc central angle. The total central angle of a circle is 360 degrees. Given the central angle of the minor - arc is 150 degrees, the central angle of the major - arc is \(360 - 150=210\) degrees.

The formula for arc length \(s = r\theta\) (where \(r\) is the radius and \(\theta\) is the central angle in radians). Convert 210 degrees to radians: \(\theta = 210\times\frac{\pi}{180}=\frac{7\pi}{6}\) radians, and \(r = 10\) units.

Then \(s=r\theta=10\times\frac{7\pi}{6}=\frac{35\pi}{3}\) units.

So the answer is c. \(\frac{35\pi}{3}\) units