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

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Chapter 1- Number SystemChapter 9-Areas of parallelogram and triangles
Chapter 2-PolynomialChapter 10-Circles
Chapter 3- Coordinate GeometryChapter 11-Construction
Chapter 4- Linear equations in two variablesChapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s GeometryChapter 13-Surface Areas and Volumes
Chapter 6-Lines and AnglesChapter 14-Statistics
Chapter 7-TrianglesChapter 15-Probability
Chapter 8- Quadrilateral

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Chapter 5-Fundamental unit of lifeChapter 13-Why do we fall ill ?
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Chapter 1-Real numberChapter 9-Some application of Trigonometry
Chapter 2-PolynomialChapter 10-Circles
Chapter 3-Linear equationsChapter 11- Construction
Chapter 4- Quadratic equationsChapter 12-Area related to circle
Chapter 5-Arithmetic ProgressionChapter 13-Surface areas and Volume
Chapter 6-TriangleChapter 14-Statistics
Chapter 7- Co-ordinate geometryChapter 15-Probability
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Chapter 4- Carbon and its CompoundsChapter 12- Electricity
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Chapter 7-Control and CoordinationChapter 15-Environment
Chapter 8- How do organisms reproduce?Chapter 16-Management of Natural Resources

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Chapter 1-SetsChapter 9-Sequences and Series
Chapter 2- Relations and functionsChapter 10- Straight Lines
Chapter 3- TrigonometryChapter 11-Conic Sections
Chapter 4-Principle of mathematical inductionChapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbersChapter 13- Limits and Derivatives
Chapter 6- Linear InequalitiesChapter 14-Mathematical Reasoning
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