#### Answer

about 11.62 in

#### Work Step by Step

Arc length s (for central angle $\theta$):$ \quad s=r\theta$, where $\theta$ is in radians
Converting between Degrees and Radians
1. Multiply a degree measure by $\displaystyle \frac{\pi}{180}$ radian and simplify to convert to radians.
2. Multiply a radian measure by $\displaystyle \frac{180^{\mathrm{o}}}{\pi}$ and simplify to convert to degrees.
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The weight will be raised for the length of the arc of the pulley as it rotates through the given angle.
The angle needs to be in radians
$\displaystyle \theta=(71+\frac{50}{60})\cdot\frac{\pi}{180}$
$ s=r\displaystyle \theta=9.27(71+\frac{50}{60})\cdot\frac{\pi}{180}\approx$11.6220602226
... about 11.62 in.