Circles and their arcs

  • Thread starter LocationX
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  • #1
147
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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?
 

Answers and Replies

  • #2
Diane_
Homework Helper
390
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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.
 
  • #3
759
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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]
 
  • #4
147
0
what if the arc was in radians? then would there be pi^2?
 
  • #5
147
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oh okay bomba, that's what I thought. thanks all
 

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