Question

1. if a central angle measures π/4 radians and the radius of the circle is 10 cm, what is the arc length? a. 10π cm b. 5π/2 cm c. 2π/3 cm d. 5π cm

Explanation:

Step1: Recall the arc - length formula

The formula for the arc length \(s\) of a circle is \(s = r\theta\), where \(r\) is the radius and \(\theta\) is the central angle in radians.

Step2: Substitute the given values

Given \(r = 10\space cm\) and \(\theta=\frac{\pi}{4}\) radians. Then \(s=10\times\frac{\pi}{4}=\frac{10\pi}{4}=\frac{5\pi}{2}\space cm\)

Answer:

b. \(\frac{5\pi}{2}\space cm\)