Question

The central angle of a circle measures 2π/7 radians and intercepts an arc of 4πyd. What is the radius of a circle.

Answer 1

r = 14 yd

Step-by-step explanation:

`\begin{gathered} The\text{ }central\text{ }angle,\theta=(2\pi)/(7) \\ \text{The length of arc, }s=4\pi yd \\ \text{The radius of the circle, }r=? \end{gathered}`

Note, the length of an arc is given by:

`s=r\theta`
`\begin{gathered} r=(s)/(\theta) \\ r=4\pi/(2\pi)/(7) \\ r=4\pi*(7)/(2\pi) \\ r=(28\pi)/(2\pi) \\ r=14\text{ yd} \end{gathered}`

Hence, the radius of the circle is 14 yd.