Circles: Area of a Sector
Master every SAT question on sectors — from basic formulas to composite-figure problems
SAT Math
Geometry
Medium–Hard Difficulty
1. What Is a Sector?
Definition
A sector is the region of a circle bounded by two radii and the arc between them — think of a "pie slice."
Parts of a Sector
- Two radii — the straight edges from center to circle
- Arc — the curved edge on the circle
- Central angle ($\theta$) — the angle formed at the center by the two radii
Sector vs. Segment
Sector = "pie slice" (bounded by two radii and an arc)
Segment = region between a chord and its arc
Segment = region between a chord and its arc
Types of Sectors
| Type | Central Angle |
|---|---|
| Minor sector | $\theta < 180°$ |
| Major sector | $\theta > 180°$ |
| Semicircular sector | $\theta = 180°$ |
Interactive: Drag the slider to change the central angle
Interactive visualization — available in the full lesson
2. Sector as a Fraction of the Circle
$$\text{Fraction} = \frac{\theta}{360°} \quad\text{(degrees)}\qquad\text{or}\qquad \frac{\theta}{2\pi} \quad\text{(radians)}$$
A sector is simply a fraction of the full circle. The fraction equals the ratio of the central angle to the full angle.
Quick Reference Table
| Central Angle $\theta$ | Fraction of Circle | Simplified |
|---|---|---|
| $30°$ | $30/360$ | $1/12$ |
| $45°$ | $45/360$ | $1/8$ |
| $60°$ | $60/360$ | $1/6$ |
| $72°$ | $72/360$ | $1/5$ |
| $90°$ | $90/360$ | $1/4$ |
| $120°$ | $120/360$ | $1/3$ |
| $180°$ | $180/360$ | $1/2$ |
| $270°$ | $270/360$ | $3/4$ |
Fraction Visualization
Interactive visualization — available in the full lesson