Solve the problem.
-Find the radius (to the nearest hundredth of a millimeter) of a pulley if rotating the pulley $55.21 ^ { \circ }$ raises the pulley $17.5 \mathrm {~mm}$.
A) $18.26 \mathrm {~mm}$
B) $18.16 \mathrm {~mm}$
C) $18.06 \mathrm {~mm}$
D) $17.96 \mathrm {~mm}$

Question

Quizplus · Accepted Answer

The arc length $s$ of a circle can be found using the formula $s = r\theta$, where $r$ is the radius and $\theta$ is the angle in radians. To solve for $r$, rearrange the formula to $r = \frac{s}{\theta}$. First, convert $55.21^\circ$ to radians: $55.21^\circ \times \frac{\pi}{180^\circ} \approx 0.963495$ radians. Then, use the given arc length $s = 17.5 \, \text{mm}$ to find $r$: $r = \frac{17.5}{0.963495} \approx 18.16 \, \text{mm}$.

Solve the Problem 55.21∘55.21 ^ { \circ }55.21∘ Raises the Pulley 17.5 mm17.5 \mathrm {~mm}17.5 mm

Solve the Problem $55.21 ^ { \circ }$ Raises the Pulley $17.5 \mathrm {~mm}$