NCERT Class 10 Mathematics Mathematics: Chapter 11 — MATHEMATICS
This chapter, NCERT Class 10 Mathematics Chapter 11, introduces students to the concepts of sectors and segments of a circle. It defines a sector as the region enclosed by two radii and an arc, and a segment as the region enclosed by a chord and an arc. The chapter distinguishes between minor and major sectors and segments. It then derives the formula for the area of a sector with a central angle θ as (θ/360°) * πr², and the formula for the length of an arc of a sector as (θ/360°) * 2πr. This foundational knowledge is crucial for solving problems involving areas and perimeters of circular regions in geometry, aiding CBSE students in their mathematical understanding.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 10 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 11 — MATHEMATICS |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 547 |
Learning outcomes
- Define and differentiate between sectors and segments of a circle.
- Identify minor and major sectors and segments.
- Derive and apply the formula for the area of a sector.
- Derive and apply the formula for the length of an arc of a sector.
Vocabulary
| Word | Meaning |
|---|---|
| Sector | The portion of a circular region enclosed by two radii and the corresponding arc. |
| Segment | The portion of a circular region enclosed between a chord and the corresponding arc. |
| Minor Sector | The sector with a smaller area, corresponding to an angle less than 180 degrees. |
| Major Sector | The sector with a larger area, corresponding to an angle greater than 180 degrees. |
| Minor Segment | The segment with a smaller area, formed by a chord and its corresponding minor arc. |
| Major Segment | The segment with a larger area, formed by a chord and its corresponding major arc. |
| Arc Length | The distance along the curved line forming part of the circumference of a circle. |
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Practice questions
- What is a sector of a circle? Answer: A sector of a circle is the portion of the circular region enclosed by two radii and the corresponding arc.
- What is a segment of a circle? Answer: A segment of a circle is the portion of the circular region enclosed between a chord and the corresponding arc.
- Write the formula for the area of a sector with angle θ (in degrees) and radius r. Answer: Area of sector = (θ/360°) * πr²
- Write the formula for the length of an arc of a sector with angle θ (in degrees) and radius r. Answer: Arc length = (θ/360°) * 2πr
Frequently asked questions
What is the difference between a sector and a segment?
A sector is formed by two radii and an arc, while a segment is formed by a chord and an arc.
How is the area of a sector calculated?
The area of a sector is calculated using the formula: (θ/360°) * πr², where θ is the central angle in degrees and r is the radius.
What is the formula for the length of an arc of a sector?
The length of an arc of a sector is calculated using the formula: (θ/360°) * 2πr, where θ is the central angle in degrees and r is the radius.
What is meant by 'minor' and 'major' in relation to sectors and segments?
'Minor' refers to the smaller part (sector or segment), and 'major' refers to the larger part.
What is the angle of a major sector?
The angle of a major sector is 360° minus the angle of the corresponding minor sector.
Related resources
Important topics
Topics covered
NCERT Class 10 Mathematics — Mathematics — Chapter 11 — MATHEMATICS. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.