Class 10 Maths · Chapter 11 · Topic 1 of 4
Know which circular part is being measured
Name the region before choosing an area or boundary formula.
Ideas you’ll use
- Sector and segment
- A sector is enclosed by two radii and their arc. A segment is enclosed by a chord and its arc.
Understand it, one idea at a time
Choose an idea. Follow its reason, calculation and clue in the picture.
A sector has radii on its boundary
- Orange outline
- Chord + arc for a segment; two radii + arc for a sector.
- Circle
- Drawn with equal physical radii in both directions.
Separate sector from segment
A sector has two radii and an arc. A segment has a chord and an arc.
sector: radii+arc; segment: chord+arcIn the picture: Compare the highlighted regions and their boundaries.
Read all the reasoning together
Separate sector from segment
A sector has two radii and an arc. A segment has a chord and an arc.
sector: radii+arc; segment: chord+arcUse the central angle
The minor region uses the smaller central angle. The major region is the remainder.
major angle=360°−minor angleDistinguish area from length
Area measures the filled region; perimeter traces its edge.
area in cm²; boundary length in cm
Name the region before choosing an area or boundary formula.
Worked example: A quarter circle
At 90°, the sector is a quadrant. Its chord cuts off a smaller segment; the triangle between the two radii is not part of that segmentAt 180°, each sector and corresponding segment is a semicircle. Major sector angle = 360°−minor angle.
Read the supporting explanation
For a central angle below 180°, the smaller part is the minor sector or segment. The remaining part is major. A sector includes the centre; the corresponding minor segment sits beyond the chord. An arc is only a curved line, so it has length, not area.
Go deeper: Use the stated part
When a question says major, take the larger region. If it only says sector or segment, read the diagram and given angle carefully rather than guessing.
Your turn
Try the idea yourself. Show your reasoning, then compare.
Question
Is the area between two radii and their arc a sector or a segment?
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