Circle Sector and Segment
Slices
There are two main "slices" of a circle:
- The "pizza" slice is called a Sector.
- And the Segment, which is cut from the circle by a "chord" (a line between two points on the circle).
Try Them!
Sector | Segment |
---|---|
Common Sectors
The Quadrant and Semicircle are two special types of Sector:
Half a circle is
a Semicircle.
Quarter of a circle is
a Quadrant.
Area of a Sector
You can work out the Area of a Sector by comparing its angle to the angle of a full circle.
Note: we are using radians for the angles.
This is the reasoning:
A circle has an angle of 2π and an Area of: | πr^{2} | |
A Sector with an angle of θ (instead of 2π) has an Area of: | (θ/2π) × πr^{2} | |
Which can be simplified to: | (θ/2) × r^{2} |
Area of Sector = \frac{θ }{2} × r^{2} (when θ is in radians)
Area of Sector = \frac{θ × π}{360} × r^{2} (when θ is in degrees)
Area of Segment
The Area of a Segment is the area of a sector minus the triangular piece (shown in light blue here).
There is a lengthy reason, but the result is a slight modification of the Sector formula:
Area of Segment = \frac{θ − sin(θ)}{2} × r^{2} (when θ is in radians)
Area of Segment = ( \frac{θ }{360} × π − \frac{sin(θ)}{2 }) × r^{2} (when θ is in degrees)
Arc LengthThe arc length (of a Sector or Segment) is: L = θ × r (when θ is in radians) L = (θ × π/180) × r (when θ is in degrees) |