Answer
$92.2\; cm$.
Work Step by Step
The given values are
Radius of the gear $r=22.0\; cm$
Turning angle $\theta = 240.0^{\circ}$
Convert the angle into radians.
By using the conversion factor $\frac{\pi \; rad}{180^{\circ}}$
$\theta=240.0^{\circ} \times \frac{\pi \; rad}{180^{\circ}}$
Simplify.
$\theta=\frac{4\pi }{3}\; rad$
The formula is
$s=r\theta$.
Where s is the distance a point travels on the surface of the gear.
Plug all values into the formula.
$s=(22.0 \; cm )(\frac{4\pi }{3})$.
Simplify
$s=92.2\; cm$.
