Sector: Sector of a Circle is given as part of Circle enclosed by 2 radius and arc.
In the diagram, shaded area OAB is the sector.
Here, θ is the angle subtended by the arc AB on the center O of the circle.
Area of the Sector is given as
Proof:
In whole circle, the angle θ will he 360°
Area of Circle = πr^{2}
Using Unitary Method
Area represented by 360° = πr^{2}
Area represented by
SemiCircle is a sector forming an angle 180° with center.
θ=180°
Now, Area of Semi Circle will be given as
Area of the SemiCircle = πr^{2}/2
Now, Area of Quarter Circle will be given as
Area of Quarter Circle =πr^{2}/4
Segment is defined as area enclosed by chord and arc of the circle.
In the diagram Shaded portion represents Segment AMB
Area of Segment AMB = Area of Sector OAB Area of triangle AOB
So,
perimeter of a Sector = l + 2r
Here l is length of arc and
115 videos478 docs129 tests

1. What is the formula for finding the area of a sector? 
2. How do you find the angle of a sector if the area is given? 
3. Can the area of a sector be greater than the area of the whole circle? 
4. How do you find the length of the arc of a sector? 
5. Can the angle of a sector be greater than 360 degrees? 
115 videos478 docs129 tests


Explore Courses for Class 10 exam
