Solve the problem.
-Find the radius (to the nearest hundredth of a millimeter)of a pulley if rotating the pulley 109.38° raises the pulley 42.2 mm.
A)22.01 mm
B)22.21 mm
C)22.11 mm
D)21.91 mm

Question

Quizplus · Accepted Answer

The distance raised (42.2 mm) corresponds to the arc length of the pulley's circumference for the given angle of rotation (109.38°). The formula to find the arc length $ s $ is $ s = r\theta $, where $ r $ is the radius and $ \theta $ is the angle in radians. First, convert the angle from degrees to radians: $ \theta = 109.38 \times \frac{\pi}{180} $. Then, solve for $ r $: $ r = \frac{s}{\theta} $. Plugging in the values, $ r = \frac{42.2}{109.38 \times (\pi/180)} \approx 22.11 $ mm.

Solve the Problem. -Find the Radius (To the Nearest Hundredth of a Millimeter)of