A slice of pizza
Sector of a circle
Cut the circle
A circle has a border, the arc, and a radius runs from the centre to every point of it. Take two points A and B on the border and join each to the centre O.
Joining A and B to the centre cuts the circle into two regions. What does the smaller region look like?
What this lesson covers
The idea
A sector of a circle is the region bounded by an arc and the two radii containing the endpoints of the arc.
Cut the circle
A circle has a border, the arc, and a radius runs from the centre to every point of it. Take two points A and B on the border and join each to the centre O.
Joining A and B to the centre cuts the circle into two regions. What does the smaller region look like?
- A slice of pizza
- A triangle
- A ring
Name the parts
Turn the angle if you like. Tap each part: the arc, both radii and the sector.
An arc and two radii
A sector of a circle is the region bounded by an arc and the two radii containing the endpoints of the arc.
Its border has three parts: the arc AB and the radii OA and OB. A slice of pizza is a sector: the crust is the arc and the two cut edges are radii.
Notes
A sector of a circle is the region bounded by an arc and the two radii containing the endpoints of the arc.
Check yourself
A sector is bounded by one arc and some radii. How many radii are part of its border?
Answer: 2
The arc AB has two endpoints, A and B, so there are 2 radii: OA and OB.
Which region is a sector?
A circle is cut along one diameter. Is each half a sector?
Which three parts make the border of the sector OAB?
- The whole border of the circle. The border is the circumference. A sector is a region, and it has two radii on its edge.
- The region between an arc and the two radii to its endpoints — correct. Yes. That is a slice of pizza.
- The region between an arc and a straight line across the circle that is not through the centre. That region is bounded by an arc and a chord, not by two radii. It is a different piece, called a segment.
- No. A sector must have a corner smaller than a straight angle. A sector can have any angle at the centre, including 180°.
- No. A sector has no straight edges. A sector has two straight edges, the two radii.
- Yes. The arc is half the circle and the two radii lie along the diameter — correct. Yes. The two radii OA and OB lie on the same line, and the sector is a semicircular disc.
- Arc AB, radius OA, radius OB — correct. Yes. The arc, and the two radii that join its endpoints to the centre.
- Arc AB and chord AB. Arc AB with chord AB bounds a segment, not a sector.
- Radius OA, radius OB and chord AB. The curved arc is part of a sector border, not the straight chord.