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.

Question

Mathematics

Anahi Pittman

23 December, 04:00

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.

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Reina Wolfe · Answer 1

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