Sector of a Circle

In this page sector of a circle we are going to see the definition of sector in a circle and its classification.

Definition of a Sector:

A part of the interior of a circle enclosed by an arc and two radii is called a sector of a given circle. 

Consider a sector of a circle whose central angle measure. ∠AOB = θ and radius "r" and length of arc AB is known as L.

There are two types of sectors. Those are

(i) Major sector

(ii) Minor sector

Major sector:

A larger part occupied by two radii is called the major sector. A major sector has central angle which is more than 180°.

Minor sector:

A smaller part occupied by two radii is called the minor sector. A minor sector has central angle which is less than 180°.

Quadrant:

A part occupied by two radii with central angle 90° is called quadrant. In other words we can define quadrant as one fourth of the circle.

Semicircle:

A part occupied by two radii with central angle 180° is called the semicircle.

Now we are going to have a set of question in which you have to choose which is major sector and which is minor sector.

Question 1:

Identify the major sector in the below diagram.

Options :

(A) ACB

(B) AOB

Answer:

Here ACB is the major part of the circle so it is called a major sector.

Question 2:

Identify the minor sector in the below diagram.

Options :

(A) ABC

(B) AOC

Answer:

Here AOC is the minor part of the circle so it is called a minor sector.

Question 3:

If the circumference of a circle is 8 units and arc length of major sector is 5 units then find the length of minor sector.

Options:

(A) 3 units

(B) 7 units

(C) 5 units

Answer:

The length of minor sector is 3 units. Because circumference means length of the circle by subtracting  the length of the major sector from the circumference we can get the length of minor sector.





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