---
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knowledge_type: "chapter"
entity_type: "chapter"
id: "69f86a1b293c3123114dbd8a"
title: "Areas Related to Circles"
board: "CBSE"
curriculum: "CBSE"
class: "Class 10"
subject: "Mathematics"
book: "Mathematics"
chapter: "Areas Related to Circles"
chapter_slug: "areas-related-to-circles"
canonical_url: "https://www.edzy.ai/cbse-class-10-mathematics-areas-related-to-circles"
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source: "Edzy"
version: 1
last_updated: "2026-06-22"
---

# Areas Related to Circles
In this chapter, students will learn about the areas related to circles, specifically focusing on sectors and segments. By the end of the chapter, key formulas for calculating the areas of these parts of the circle will be discussed, along with examples to solidify understanding.

---

## Knowledge Snapshot

| Field | Details |
| :--- | :--- |
| Class | Class 10 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Areas Related to Circles |
| Pages | 154-160 |

---

## Chapter Summary

### Short Summary
This chapter covers the definitions and formulas associated with sectors and segments of circles, their areas, and relevant examples.

### Detailed Summary
Students will explore the concepts of sectors and segments within circles. A sector is defined as the area enclosed by two radii and an arc, whereas a segment is defined as the area enclosed by a chord and an arc. Detailed formula derivations for calculating areas of sectors and segments will be provided along with practical examples to illustrate the concepts.

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## Topic-Wise Explanation

### Areas of Sector and Segment of a Circle
This topic introduces the concepts of sectors and segments, defining their boundaries and properties. The area of a sector can be calculated using the formula:
$$Area\ of\ the\ sector\ of\ angle\ q = rac{\pi rq}{360}$$, where $r$ is the radius and $q$ is the angle in degrees. Length of the arc is given by:
$$Length\ of\ an\ arc\ = rac{2\pi rq}{360}$$. The area of a segment is calculated as:
$$Area\ of\ the\ segment\ = Area\ of\ the\ sector - Area\ of\ triangle$$.

---

## Core Ideas

| Idea | Explanation |
| :--- | :--- |
| Sector | Area enclosed by two radii and an arc. |
| Segment | Area between a chord and the corresponding arc. |

---

## Key Concepts

| Concept | Meaning |
| :--- | :--- |
| Area of Sector | Formula to compute the area based on radius and angle of the sector. |
| Area of Segment | The area of the sector minus the area of the triangle formed by the radius and the chord. |

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## Important Points for Revision

* Area of a sector: $A = rac{\pi rq}{360}$
* Length of an arc: $L = rac{2\pi rq}{360}$
* Area of a segment: $A = Area\ of\ the\ sector - Area\ of\ triangle$
* Minor and Major sectors are defined based on the angle of the sectors.
* Minor and Major segments are defined similarly based on associated chords.

---

## Vocabulary and Glossary

| Word / Phrase | Meaning |
| :--- | :--- |
| Sector | Part of a circle defined by two radii and an arc. |
| Segment | Part of a circle defined by a chord and an arc. |

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## Practice Questions

### Short Answer Questions
1. What is the area of a sector with radius 6 cm and an angle of 60°?
2. Find the area of a segment if the radius is 21 cm and the central angle is 120°.
3. Calculate the length of an arc for a sector of angle 30°.
4. How do you determine the area of a triangle formed within a segment?
5. Explain the difference between minor and major segments in a circle.

### Long Answer Questions
1. Derive the formula for the area of a sector and provide an example calculation.
2. Explain how to find the area of a segment and give a worked-out example.
3. Calculate the area of the entire circle given the radius, and then find the areas of the sectors and segments.

---

## Related Concepts
None.

---

## Source Attribution

| Field | Value |
| :--- | :--- |
| Source | Edzy |
| Reference Type | examSubjectBookChapter |
| Reference ID | 69f86a1b293c3123114dbd8a |
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