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Chapter 11 - Areas Related to Circles Class 10 Maths Notes
Understand Areas Related to Circles with concise notes from ALLEN's expert for effective revision.
Areas Related to Circles Class 10 Maths helps you understand how to calculate the area and circumference of circles, sectors, and segments using simple formulas and step-by-step methods. It also covers how to solve questions involving different combinations of circular figures.
CBSE Maths Class 10 Chapter 11 – Areas Related to Circles Notes make it easier to learn and revise important concepts such as the area and circumference of a circle, the area of a sector and segment, and their applications. You can download these CBSE Class 10 Maths Notes PDF to understand key formulas, follow step-by-step solutions, and practise important questions for your Class 10 board exams.
1.0Introduction to Areas Related to Circles Class 10 Maths
A circle is a closed curve in which all points are equidistant from a fixed point, which is 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.
Read More on: Areas Related to Circles Class 10 Maths
2.0CBSE Class 10 Maths Chapter 11 Area Related to Circles - Detailed Revision Notes
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;
3.0Chapter 11: Area Related to Circles – Key Notes
Areas of a sector and a 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.
4.0Areas Related to Circles Class 10 Maths Solved 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 =
5.0Download Class 10 Maths CBSE Notes - ALL Chapters
Get Class 10 Maths CBSE Notes for all chapters, prepared by ALLEN SUbject Experts for effective learning and revision. Get clear explanations of important concepts, formulas, theorems, and key topics covered in the CBSE Class 10 Maths syllabus. Use these chapter-wise notes to strengthen your understanding, revise important concepts, and prepare confidently for the CBSE Board Exams.
6.0Study Resources for CBSE Class 10 Maths
7.0Key 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.