Expert: Richard J. Raridon - 2/27/2007

Question
Hello Richard,
          I have two questions for you in which I cannot answer on my homework for the life of me. All help would be appreciated.

1.I have wheel with 27 spokes that are all evenly spaced, with the 4 following questions for the wheel.
A. Finding the measure to each central angle in degrees and radians.
B. If the radius is 76 feet, find the circumference.
C. Find the length of each arc between the spokes.
D. Find the area of each section formed by the spokes and arc.

Yeah, totally lost on this one.

Second Question:
Degree of Curvature...
A railroad curve has  central angle that is subtended by a chord of 100 ft.  Supposing a portion of track has a curvature of 42 degress...

A. what is the radius of the curve?
B. What is the length of the arc determined by the 100ft chord?
C. What is the area of the portion of the circle bounded by the arc and the 100 ft. chord?

Any and all help is greatly appreciated, I could use a lot of it. Thank You  

Answer
A. have you learned that the total number of degrees in a circle is 360?   total no. of radians = 2pi?
central angle = 360/27 = 13.33 degrees
central angle = 2pi/27 = 0.233 radians
B. C = 2pi(r) = 447.5 ft.
C. 447.5/27 = 17.7 ft
D. total area = pi(r^2) = 18146 ft^2
area of section = 18146/27 = 672 ft^2
A. sin(21) = 50/r so r = 139.52 ft
B. S = rA where A is the angle in radians
S = 139.52(42/57.29) = 102.3 ft
C. Area = area of two triangles with height = 50 and
base = 130.25 = 1302.5 ft^2