Question

How long is the arc intersected by a central angle of StartFraction pi Over 3 EndFraction radians in a circle with a radius of 6 ft? Round your answer to the nearest tenth. Use 3. 14 for Pi. 1. 0 ft 5. 7 ft 6. 3 ft 7. 0 ft.

Answer 1

$\textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=6\\ \theta =\frac{\pi }{3} \end{cases}\implies s=6\cdot \cfrac{\pi }{3}\implies s=2\pi \implies s\approx 6.3$