SOLUTION: The central angle corresponding to a circular brake shoe measures 60°. To two decimal places, how long is the curved surface of the brake shoe if the length of the radius is 9 in.

Algebra ->  Formulas -> SOLUTION: The central angle corresponding to a circular brake shoe measures 60°. To two decimal places, how long is the curved surface of the brake shoe if the length of the radius is 9 in.      Log On


   

Question 1194246: The central angle corresponding to a circular brake shoe measures 60°. To two decimal places, how long is the curved surface of the brake shoe if the length of the radius is 9 in.?
Answer by math_tutor2020(3817) About Me  (Show Source):
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Answer: 9.42 inches

Work Shown:
x = central angle = 60 degrees
r = radius = 9 inches
L = arc length
L = (x/360)*2*pi*r
L = (60/360)*2*pi*9
L = 3*pi
L = 9.42477796076938
L = 9.42

Notes:
  • I used the calculator's stored version of pi to get the most accuracy possible. If your teacher requires you to use the approximation pi = 3.14, then be sure to follow those instructions.
  • The x/360 portion takes a fractional amount of the circumference C = 2*pi*r; hence the (x/360)*2*pi*r