Solve the problem.
-Two wheels are rotating in such a way that the rotation of the smaller wheel causes the larger wheel to rotate. The radius of the smaller wheel is 8.8 centimeters and the radius of the larger wheel
Is 16.9 centimeters. Through how many degrees (to the nearest hundredth of a degree)will the
Larger wheel rotate if the smaller one rotates 180°?
A)94.73°
B)93.73°
C)95.73°
D)93.63°

Question

Quizplus · Accepted Answer

The rotation angle of the larger wheel can be found by using the ratio of the circumferences of the two wheels. The circumference of a circle is given by $C = 2\pi r$, where $r$ is the radius. The ratio of the circumferences of the smaller to the larger wheel is $\frac{2\pi(8.8)}{2\pi(16.9)} = \frac{8.8}{16.9}$. If the smaller wheel rotates 180°, the larger wheel will rotate a proportionally smaller angle due to its larger circumference. The angle of rotation for the larger wheel is $180° \times \frac{8.8}{16.9} \approx 93.73°$.

Solve the Problem. -Two Wheels Are Rotating in Such a Way That the Way