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Finding Perimeter/Circumference of part of a circle

  1. Apr 19, 2010 #1
    1. The problem statement, all variables and given/known data
    The inner radius is measured from a point A and is 2.9 m. The outer radius is measured from the same point A and is 6.5 m. The angle at A is 110*. What is the Perimeter of the shaded area in meters? What is the area of the shaded are in square meters?


    2. Relevant equations
    C=2rpi


    3. The attempt at a solution
    Just for part A I tried to find the total circumference as if the circle was a full 360* and then multiplied the resulting answer by the ratio of 110*/360*. The answer was incorrect. The answers are suppose to be 25.3 m and 32.5 m^2
     
  2. jcsd
  3. Apr 19, 2010 #2

    Mark44

    Staff: Mentor

    From your description, it seems that you need to find the perimeter and area of a section of a ring or annulus.

    The circumference of a circle is C = r * 2pi. The arc length along the portion of a circle subtended by an arc whose measure is theta (in radians) is r * theta.

    The area of an annulus is pi(R^2 - r^2), where R and r represent the outer and inner radii respectively.
     
  4. Apr 19, 2010 #3
    We know the area of a circle as:
    [PLAIN]https://dl.dropbox.com/u/4645835/MATH/Area%20of%20Circle.gif [Broken]

    Part B:
    We want to find the area of the shaded portion. So, we find the area of the outside circle and subtract from it the area of the inside circle.

    [PLAIN]https://dl.dropbox.com/u/4645835/MATH/Worked.gif [Broken]
     
    Last edited by a moderator: May 4, 2017
  5. Apr 19, 2010 #4

    Mark44

    Staff: Mentor

    Well, I don't know what the drawing looks like, so I don't know exactly what the problem is. How does the angle of 110 degrees enter into the problem?
     
  6. Apr 20, 2010 #5
    I imagine it as a larger circle around a smaller circle. The shaded region they are referring to would be the area enclosed by the two circles. The given angle...according to my interpretation...is between the 0 degree line and the radii extending from point A.
     
  7. Apr 20, 2010 #6

    Mark44

    Staff: Mentor

    The problem doesn't include a picture?
     
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