Area of the segment and sector of a circle - Future Study Point

Area of the segment and sector of a circle

areas of segments and sectors

Segment and sector of a circle

You are familiar with some methods of finding the area of plane figures like triangle, square, rectangle, parallelogram, rhombus, and of the circle. Here the area of segment and sector of the circle is of great importance in our day to life like areas of the rounded figure as an example, wheel excel, and other rounded tools and machines. The segment and sector are the part of the rounded figure are needed in manufacturing different types of tools used in machines and architectural designs of bridges and buildings, so the area of segments and sectors of the circle is introduced in the 10-grade syllabus of every school board.

areas of segments and sectors

 

 

NCERT Solutions Class 10 Science from chapter 1 to 16

Area of the segment and sectors is the topic referred from chapter 12 of the class 10 NCERT  book prescribed by CBSE a reputed board of India for school education.

Sector of circle :

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Sector of circle

 

The area covered by two radii and the corresponding arc of the circle is known as sector.

360° angle around the centre corresponds to the area 

1° angle around the circle corresponds to the area 

θ angle around the circle correspond to the area 

Hence the area of a sector

Where θ is the angle between two radii of  the circle.

Type of sectors : Sectors of circles are of two kinds (a) Minor sector (b) Major sector

Minor sector: The shaded region  in above figure is minor sector i.e The smaller sector is known as minor sector.

Major sector: The unshaded region  in above figure is major sector i.e The larger sector is known as major sector.

Area of major sector = Area of circle – area of minor sector

Segment of a circle :

The area covered by the chord of a circle and corresponding arc known as segment.

Area of segment = area of sector – area of triangle covered by two radii and corresponding chord of the circle

Let the angle subtended by the two radii is = θ

segment of circle

∠AOM = θ/2 (OM⊥ AB)

AM = r sinθ/2

AB = 2AM=2r sinθ

OM = r cosθ/2

Area of ΔAOB

Since ,2sin θ cos θ =sin2θ

Hence area of ΔAOB = 1/2 r² sinθ

We know area of sector

So, area of segment

Hence Area of segment

Type of segment

(a) Minor segment: The smaller segment of the circle is known as minor segment i.e The shaded region in above figure is known as minor segment.

(b) Major segment: The larger segment of the circle is known as major segment i.e The unshaded region in above figure is known as major segment.

The area of larger segment = Area of circle – area of minor sector

Length of arc :

Arc of the circle,l

 

Let the length of arc corresponding to two radii of circle is l.

360° angle corresponds to

1° angle corresponds to   

θ angle corresponds to   

Hence the length of arc corresponding to two radii   

Type of Arc

(a) Minor arc: The smaller arc of the circle is known as minor arc, in the figure l is the length of minor arc.

(b) Major arc: The larger arc of the circle is known as major arc

The length of major arc = Circumference of the circle – The length of minor arc

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NCERT Solutions of Science and Maths for Class 9,10,11 and 12

NCERT Solutions for class 9 maths

Chapter 1- Number System Chapter 9-Areas of parallelogram and triangles
Chapter 2-Polynomial Chapter 10-Circles
Chapter 3- Coordinate Geometry Chapter 11-Construction
Chapter 4- Linear equations in two variables Chapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s Geometry Chapter 13-Surface Areas and Volumes
Chapter 6-Lines and Angles Chapter 14-Statistics
Chapter 7-Triangles Chapter 15-Probability
Chapter 8- Quadrilateral

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Chapter 1-Matter in our surroundings Chapter 9- Force and laws of motion
Chapter 2-Is matter around us pure? Chapter 10- Gravitation
Chapter3- Atoms and Molecules Chapter 11- Work and Energy
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Chapter 5-Fundamental unit of life Chapter 13-Why do we fall ill ?
Chapter 6- Tissues Chapter 14- Natural Resources
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Chapter 1-Real number Chapter 9-Some application of Trigonometry
Chapter 2-Polynomial Chapter 10-Circles
Chapter 3-Linear equations Chapter 11- Construction
Chapter 4- Quadratic equations Chapter 12-Area related to circle
Chapter 5-Arithmetic Progression Chapter 13-Surface areas and Volume
Chapter 6-Triangle Chapter 14-Statistics
Chapter 7- Co-ordinate geometry Chapter 15-Probability
Chapter 8-Trigonometry

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Chapter 2- Acid, Base and Salt Chapter 10- Light reflection and refraction
Chapter 3- Metals and Non-Metals Chapter 11- Human eye and colorful world
Chapter 4- Carbon and its Compounds Chapter 12- Electricity
Chapter 5-Periodic classification of elements Chapter 13-Magnetic effect of electric current
Chapter 6- Life Process Chapter 14-Sources of Energy
Chapter 7-Control and Coordination Chapter 15-Environment
Chapter 8- How do organisms reproduce? Chapter 16-Management of Natural Resources

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Chapter 1-Sets Chapter 9-Sequences and Series
Chapter 2- Relations and functions Chapter 10- Straight Lines
Chapter 3- Trigonometry Chapter 11-Conic Sections
Chapter 4-Principle of mathematical induction Chapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbers Chapter 13- Limits and Derivatives
Chapter 6- Linear Inequalities Chapter 14-Mathematical Reasoning
Chapter 7- Permutations and Combinations Chapter 15- Statistics
Chapter 8- Binomial Theorem  Chapter 16- Probability

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Chapter 1-Relations and Functions Chapter 9-Differential Equations
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Chapter 3-Matrices Chapter 11 – Three Dimensional Geometry
Chapter 4-Determinants Chapter 12-Linear Programming
Chapter 5- Continuity and Differentiability Chapter 13-Probability
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