Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal
places.
-A car wheel has a 16-inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward 5 ft?
A) $214.9 ^ { \circ }$
B) $219.9 ^ { \circ }$
C) $224.9 ^ { \circ }$
D) $229.9 ^ { \circ }$

Question

Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal
places.
-A car wheel has a 16-inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward 5 ft? 
A) $214.9 ^ { \circ }$
B) $219.9 ^ { \circ }$
C) $224.9 ^ { \circ }$
D) $229.9 ^ { \circ }$

Quizplus · Accepted Answer

First, convert 5 ft to inches: 5 ft = 60 inches. The arc length formula is $ s = r \theta $, where $ s $ is the arc length, $ r $ is the radius, and $ \theta $ is the angle in radians. So, $ \theta = \frac{s}{r} = \frac{60}{16} = 3.75 $ radians. Convert radians to degrees: $ 3.75 \times \frac{180}{\pi} \approx 214.9^\circ $.

Find the Length of the Arc on a Circle of Radius