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Circles and their arcs

  1. Oct 2, 2005 #1
    what is the formula to find a sector in a circle?

    so I'm given the radius and the arc of angle 60 degrees. To find the area in that arc, the forumla is something along the lines of:

    [tex]A=\frac{r^2}{2} * arc[/tex] so...
    [tex]A=\frac{r^2}{2} * \frac{\pi}{3}[/tex]

    is this right?
  2. jcsd
  3. Oct 2, 2005 #2


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    The area of a circle is pi r^2, yes? So if you have, say, 30 degrees of central angle, the area will be 30/360 of the area of the total circle. In that case, you'd take (30/360) * pi * r^2.

    The sector is just a fraction of the circle, so use a fraction of the area formula.
  4. Oct 2, 2005 #3
    Well, if you're given the radius and the central angle, then the sector area is just:
    ~in degrees,

    [tex] A = \frac{{\pi r^2 \theta}}{{360^\circ }} [/tex]
    ~but if [tex] \theta [/tex] is in radians, then

    [tex] A = \frac{{r^2 \theta }}{2} [/tex]
  5. Oct 2, 2005 #4
    what if the arc was in radians? then would there be pi^2?
  6. Oct 2, 2005 #5
    oh okay bomba, that's what I thought. thanks all
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