
Define the circle segment and sector of a circle.
Answer
506.4k+ views
Hint: Segment of a circle is the region bounded by a chord and the arc subtended by the chord.
Sector of the circle looks like a pizza slice.
Complete step by step solution: Segment is the region of a circle bounded by chord and an arc.
The segments are explained in two parts:
As we show in the above diagram a line divides the circle in two parts in which the biggest part of the circle is called the major segment.
Or the lower part or portion is known as a minor segment.
We also calculate the area of segment:
The area of the segment is equal to area of sector minus of area of triangular piece.
\[Area\,\,of\,\,segment = \dfrac{{\left( {\theta - \sin \theta } \right) \times {r^2}}}{2}\,\,\left[ {When\,\,\theta \,\,in\,\,radians} \right]\]
\[Area\,\,of\,\,segment = \left( {\dfrac{{\theta \times \pi }}{{360}} - \dfrac{{\sin \theta }}{2}} \right) \times {r^2}\] (when \[\theta \]is in degrees)
Sector of Circle
The shaded region is the sector of circle.
A sector is created by the central angle formed with two radii and it includes the area inside the circle from that center point to the circle itself. The portion of the circle's circumference bounded by the radii, the arc, is part of the sector.
Common Sectors
The quadrant and semicircle are two special types of sector:
Area of sector\[ = \left( {\dfrac{{\theta ^\circ }}{{360^\circ }}} \right) \times \pi \times {r^2}\]
Where
\[\theta ^\circ \] = degree of the circle
\[R{\text{ }} = {\text{ }}radius{\text{ }}of{\text{ }}the{\text{ }}circle\]
Note: A circle has an angle of\[2\pi \]and an area of $ [ \pi \times {r^2}] $ . A sector has an angle of\[\theta \]instead of \[2\pi \] ,so it has an area which can be simplified to:\[\dfrac{\theta }{2} \times {r^2}\]
Sector of the circle looks like a pizza slice.
Complete step by step solution: Segment is the region of a circle bounded by chord and an arc.

The segments are explained in two parts:
As we show in the above diagram a line divides the circle in two parts in which the biggest part of the circle is called the major segment.
Or the lower part or portion is known as a minor segment.
We also calculate the area of segment:
The area of the segment is equal to area of sector minus of area of triangular piece.

\[Area\,\,of\,\,segment = \dfrac{{\left( {\theta - \sin \theta } \right) \times {r^2}}}{2}\,\,\left[ {When\,\,\theta \,\,in\,\,radians} \right]\]
\[Area\,\,of\,\,segment = \left( {\dfrac{{\theta \times \pi }}{{360}} - \dfrac{{\sin \theta }}{2}} \right) \times {r^2}\] (when \[\theta \]is in degrees)

Sector of Circle
The shaded region is the sector of circle.

A sector is created by the central angle formed with two radii and it includes the area inside the circle from that center point to the circle itself. The portion of the circle's circumference bounded by the radii, the arc, is part of the sector.
Common Sectors
The quadrant and semicircle are two special types of sector:

Area of sector\[ = \left( {\dfrac{{\theta ^\circ }}{{360^\circ }}} \right) \times \pi \times {r^2}\]
Where
\[\theta ^\circ \] = degree of the circle
\[R{\text{ }} = {\text{ }}radius{\text{ }}of{\text{ }}the{\text{ }}circle\]
Note: A circle has an angle of\[2\pi \]and an area of $ [ \pi \times {r^2}] $ . A sector has an angle of\[\theta \]instead of \[2\pi \] ,so it has an area which can be simplified to:\[\dfrac{\theta }{2} \times {r^2}\]
Recently Updated Pages
Master Class 9 General Knowledge: Engaging Questions & Answers for Success

Earth rotates from West to east ATrue BFalse class 6 social science CBSE

The easternmost longitude of India is A 97circ 25E class 6 social science CBSE

Write the given sentence in the passive voice Ann cant class 6 CBSE

Convert 1 foot into meters A030 meter B03048 meter-class-6-maths-CBSE

What is the LCM of 30 and 40 class 6 maths CBSE

Trending doubts
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

List some examples of Rabi and Kharif crops class 8 biology CBSE

What is the feminine gender of a stag class 8 english CBSE

How many ounces are in 500 mL class 8 maths CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

How many ten lakhs are in one crore-class-8-maths-CBSE
