# Circles and their arcs

#### LocationX

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:

$$A=\frac{r^2}{2} * arc$$ so...
$$A=\frac{r^2}{2} * \frac{\pi}{3}$$

is this right?

#### Diane_

Homework Helper
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.

#### bomba923

Well, if you're given the radius and the central angle, then the sector area is just:
~in degrees,

$$A = \frac{{\pi r^2 \theta}}{{360^\circ }}$$
------------------------------
~but if $$\theta$$ is in radians, then

$$A = \frac{{r^2 \theta }}{2}$$

#### LocationX

what if the arc was in radians? then would there be pi^2?

#### LocationX

oh okay bomba, that's what I thought. thanks all

### The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving