Question

It takes a wheel 200 feet to complete 12 revolutions. Find the length of an arc of the wheel to the nearest hundredth created by a central angle of 1 radian.

Answer 1

2.65 feet

Explanation:

Each revolution corresponds to a central angle of 2π radians, so 12 revolutions represent an arc of 24π radians. That means the arc length of 1 radian is ...

(1 rad)(200 ft)/(24π rad) ≈ 2.65 ft

The length of the arc with a central angle of 1 rad is about 2.65 feet.