NEETClass 11thClass 12thClass 12th PlusJEEClass 11thClass 12thClass 12th PlusClass 6-10Class 6thClass 7thClass 8thClass 9thClass 10thOnline CoursesDistance LearningInternational OlympiadNEETClass 11thClass 12thClass 12th PlusJEE (Main+Advanced)Class 11thClass 12thClass 12th PlusJEE MainClass 11thClass 12thClass 12th PlusClass 6-10Class 6thClass 7thClass 8thClass 9thClass 10thNEET2025202420232022JEE20262025202420232022Class 6-10JEE MainPrevious Year PapersSample PapersMock TestResultAnalysisSyllabusExam DatePercentile PredictorAnswer KeyCounsellingEligibilityExam PatternJEE MathsJEE ChemistryJEE PhysicsJEE AdvancedPrevious Year PapersSample PapersMock TestResultAnalysisSyllabusExam DateAnswer KeyEligibilityExam PatternRank PredictorNEETPrevious Year PapersSample PapersMock TestResultAnalysisSyllabusExam DateCollege PredictorAnswer KeyRank PredictorCounsellingEligibilityExam PatternBiologyNCERT SolutionsClass 6Class 7Class 8Class 9Class 10Class 11Class 12TextbooksCBSEClass 12Class 11Class 10Class 9Class 8Class 7Class 6SubjectsSyllabusNotesSample PapersQuestion PapersICSEClass 10Class 9Class 8Class 7Class 6State BoardBiharKarnatakaMadhya PradeshMaharashtraTamilnaduWest BengalUttar PradeshOlympiadMathsScienceEnglishSocial ScienceNSOIMONMTCASATInstant Online ScholarshipAIOT(NEET)TALLENTEXALLEN for SchoolsAbout ALLENBlogsNewsCareersRequest a call backBook a demo
CBSE Notes For Class 10 Maths Chapter 11 Areas Related To Circles
CBSE Notes For Class 10 Maths Chapter 11 – Areas Related To Circles help you understand how to calculate areas of sectors, segments, and combinations of figures involving circles. In this chapter, you will learn important formulas related to circumference, area of a circle, sector, and segment, along with their applications. These CBSE Notes provide clear explanations, step-by-step solutions, and key formulas to make revision easy and effective for your Class 10 board exams.
1.0Introduction to Circles
A circle is a closed curve in which all the points are equidistant from a fixed point, which is also called the centre. The distance from the centre to any point on the circle is called the radius. The area covered by a circle can be calculated using the given formula.
Where, r = radius of the circle.
Perimeter/circumference of the circle =
Diameter = 2r
2.0Download CBSE Notes for Class 10 Maths Chapter 11: Area Related to Circles - Free PDF!!
Download your CBSE Notes for Class 10 Maths Chapter 11: Areas Related to Circles in free PDF format for easy and fast revision. These notes include key formulas, clear explanations, and solved examples to help you prepare effectively for your board exams.
3.0CBSE Class 10 Maths Chapter 11 Area Related to Circles - Revision Notes
What are the sectors, segments, and lengths of an arc of a circle?
Sector of a circle
The sector is the region between two radii and the arc of a circle. Sectors are of two types:
- Minor Sector: It is the sector corresponding to an angle less than 180 degrees.
- Major Sector: This sector corresponds to an angle more than or equal to 180 degrees.
Area related to the sector:
If the angle of a sector is given by then;
Segment of a circle
A segment of a circle is the region enclosed by a chord and the arc intercepted by that chord. Essentially it's an area between the chord and the arc, part of the circle lying between the chord and the curved part of it. In maths, Segment is also of two types:
- Minor Segment: The segment is made of a chord and a minor arc.
- Major Segment: The arc greater than the semicircle created by a chord.
Area related to segment:
The area of a segment of a circle is the area of the sector minus the area of a triangle formed by two radii and the corresponding chord.
Area of segment = Area of the sector - Area of a triangle
That is,
Length of Arc of the Circle
The length of an arc is defined as the distance along the curved part of the circle between two points on the circumference as given in the figure.
The length of an arc depends upon the radius of the circle and the central angle subtended by the arc. It is denoted by l.
Area related to the length of an arc of the circle:
If the angle of a sector is given by then;
4.0CBSE Class 10 Maths Chapter 11 Area Related to Circles - Key Notes
Areas of sector and segment of a circle
Sector : The portion (or part) of the circular region enclosed by two radii and the corresponding arc of a circle is called a sector of the circle.
Segment : The portion (or part) of the circular region enclosed between a chord and the corresponding arc of a circle is called a segment of the circle.
Area of sector : Area of the sector of angle θ = θ/360 × πr²
Length of the arc : length of arc of sector of angle θ = θ/360 × 2πr
Area of segment : Area of segment APB = area of sector OAPB − area of ΔOAB = θ/360 × πr² − area of ΔOAB
Cor. 1. Area of major sector AQB = πr² − area of the minor sector OAPB = (360 − θ)/360 × πr²
Cor. 2. Area of major segment AQB = πr² − area of the minor segment APB.
Note
Area of ΔOAB with ∠AOB = θ is 1/2 r² sin θ or r² sin(θ/2) cos(θ/2)
where r is the radius of the circle and θ is the angle of the sector.
5.0Solved Problems
Question 1: The area of a sector of a circle of radius 36 cm is . Find the length of the corresponding arc of the sector.
Solution:
Question 2: In the given figure, find the area of the shaded region given that the radius of the circle that is inscribed in a square is 7.5cm.
Solution:
The Diameter of the circle = side of the square = 15cm
Area of the shaded region =Area of square-Area of circle
Question 3: A chord of a circle of radius 20 cm subtends an angle of 90° at the centre. Find the area of the corresponding major segment of the circle. (Use π = 3.14).
Solution: Area of segment = 360r2- Area of triangle
Area of minor segment = 903603.14202-122020 = 314-200=114cm2
Area of a circle = r2= 3.1420 × 20=1256cm2
Area of major segment= Area of circle-Area of minor segment
= 1256-114=1142cm2
Question 4: A calf is tied with a rope of length 6 m at the corner of a square grassy lawn of side 20 m. If the length of the rope is increased by 5.5m, find the increase in the area of the grassy lawn in which the calf can graze.
Solution: The increase in area = Difference between the two sectors of central angle 90° each and radii 11.5 m (6 m + 5.5 m) and 6 m,
So, the required increase in area =
6.0Key features of CBSE Maths Notes for Class 10 Chapter 11
- The notes are aligned with the latest CBSE Class 10 curriculum.
- A step-by-step guide is also provided, along with solved problems to help you better understand the chapter.
- Visual aids and diagrams are provided for a better understanding of concepts.
- The language used is easy to understand, making notes ideal for self-learning.