Detailed definition
Understanding Sector
A sector is the region of a circle bounded by two radii and the included arc. It is a filled slice of the circle, not just the curved edge and not the cap-shaped region cut by a chord.
Sector geometry links area and arc length to the same central angle. Once the central angle is known, the sector's share of the whole circle can be read as a fraction of 360 degrees.
This page highlights the two radii and the curved boundary together so you can see why a sector depends on the center in a way that other circle regions do not.
Key facts
Important ideas to remember
- A sector is the region bounded by two radii and the included arc.
- The center of the circle is always part of a sector because both bounding sides are radii.
- Sector area and arc length are both controlled by the same central-angle fraction of the full circle.
- A sector is a region, so it has area; an arc is only the curved boundary of that region.
Where it is used
Where sector shows up
- Use sectors in area and arc-length problems based on central-angle measure.
- Use them in pie-chart style interpretations and other proportional circle regions.
- Use sector language when the center must be included as part of the geometry.
Common mistakes
What to watch out for
- Do not confuse a sector with an arc; the sector is the filled region, not the curved edge alone.
- Do not replace one bounding radius with a chord, because that creates a segment region instead.
- Do not forget to use the central-angle fraction when moving from the whole circle to one sector.