The current San Francisco cable railway is driven by two large 14-foot-diameter drive wheels, called sheaves. Because of the figure-eight system used, the cable subtends a central angle of 270°on each sheave. Find the length of cable riding on one of the drive sheaves at any given time.
Accepted Solution
A:
The length of an arc is given by (θ/360)2πr, where θ is the angle subtended by the arc at the center and r is the radius. The angle θ in this case is 270°, while the radius is 7 feet, diameter is 14 feet Thus the length of the of the cable will be; =(270/360)× 22/7×14 = 0.75 × 44 = 33 feet