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 $4.7$ centimeters and the radius of the larger wheel is $16.1$ centimeters. Through how many degrees (to the nearest hundredth of a degree) will the larger wheel rotate if the smaller one rotates $220 ^ { \circ }$ ?
A) $64.22 ^ { \circ }$
B) $66.22 ^ { \circ }$
C) $64.12 ^ { \circ }$
D) $65.22 ^ { \circ }$

Question

Quizplus · Accepted Answer

The rotation of the wheels is inversely proportional to their radii. The formula to find the angle of rotation for the larger wheel is $\theta_{\text{large}} = \theta_{\text{small}} \times \frac{r_{\text{small}}}{r_{\text{large}}}$, where $\theta_{\text{large}}$ and $\theta_{\text{small}}$ are the angles of rotation for the large and small wheels respectively, and $r_{\text{small}}$ and $r_{\text{large}}$ are their radii. Plugging in the given values: $\theta_{\text{large}} = 220^\circ \times \frac{4.7}{16.1} \approx 64.22^\circ$.

Solve the Problem 4.74.74.7 Centimeters and the Radius of the Larger Wheel Is

Solve the Problem $4.7$ Centimeters and the Radius of the Larger Wheel Is