Question

Find the length of the arc of a circle of diameter 2 meters subtended by a central angle of

5pi/3
radians. In meters.

Answer 1

we know the diameter of it is 2, so its radius must be half that, and the central angle is 5π/3, so

`\textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=1\\ \theta =(5\pi )/(3) \end{cases}\implies s=(1)((5\pi )/(3))\implies s\approx 5.24~meters`