Areas Related to Circles Class 10 PPT

 Page 1


? You know that area of a circle of radius r is pr
2
.
? You can imagine the circular region formed by the circle 
of radius r as a sector of angle 360
o
(Because angle at the 
centre is a complete angle).
? With this assumption, we can calculate the area of the 
sector OAPB as follows:
? Area of a sector of angle 360
o
= pr
2
? So, area of a sector of angle 1
o
= pr
2
360
o
? Hence, area of a sector of angle  = pr
2 
× ?
360°
=   pr
2
?
36o°
Page 2


? You know that area of a circle of radius r is pr
2
.
? You can imagine the circular region formed by the circle 
of radius r as a sector of angle 360
o
(Because angle at the 
centre is a complete angle).
? With this assumption, we can calculate the area of the 
sector OAPB as follows:
? Area of a sector of angle 360
o
= pr
2
? So, area of a sector of angle 1
o
= pr
2
360
o
? Hence, area of a sector of angle  = pr
2 
× ?
360°
=   pr
2
?
36o°
? Length of the Arc of a sector 
You know that circumference of a circle of radius r 
is 2 pr.
You can calculate the length of the arc of sector 
OAPB as follows:
Length of the arc of a sector of angle 360
o
= 2 pr
So, length of the arc of a sector of angle 1
o
= 2 pr
360
o
Hence, length of the arc of a sector of angle ? = 
?
360
×2 pr
Page 3


? You know that area of a circle of radius r is pr
2
.
? You can imagine the circular region formed by the circle 
of radius r as a sector of angle 360
o
(Because angle at the 
centre is a complete angle).
? With this assumption, we can calculate the area of the 
sector OAPB as follows:
? Area of a sector of angle 360
o
= pr
2
? So, area of a sector of angle 1
o
= pr
2
360
o
? Hence, area of a sector of angle  = pr
2 
× ?
360°
=   pr
2
?
36o°
? Length of the Arc of a sector 
You know that circumference of a circle of radius r 
is 2 pr.
You can calculate the length of the arc of sector 
OAPB as follows:
Length of the arc of a sector of angle 360
o
= 2 pr
So, length of the arc of a sector of angle 1
o
= 2 pr
360
o
Hence, length of the arc of a sector of angle ? = 
?
360
×2 pr
?Recall that a chord of a circle divides the 
circular region into two parts. Each part is 
called a segment of the circle.
?There are two parts of area of segment :-
?Major Segment
?Minor Segment
Page 4


? You know that area of a circle of radius r is pr
2
.
? You can imagine the circular region formed by the circle 
of radius r as a sector of angle 360
o
(Because angle at the 
centre is a complete angle).
? With this assumption, we can calculate the area of the 
sector OAPB as follows:
? Area of a sector of angle 360
o
= pr
2
? So, area of a sector of angle 1
o
= pr
2
360
o
? Hence, area of a sector of angle  = pr
2 
× ?
360°
=   pr
2
?
36o°
? Length of the Arc of a sector 
You know that circumference of a circle of radius r 
is 2 pr.
You can calculate the length of the arc of sector 
OAPB as follows:
Length of the arc of a sector of angle 360
o
= 2 pr
So, length of the arc of a sector of angle 1
o
= 2 pr
360
o
Hence, length of the arc of a sector of angle ? = 
?
360
×2 pr
?Recall that a chord of a circle divides the 
circular region into two parts. Each part is 
called a segment of the circle.
?There are two parts of area of segment :-
?Major Segment
?Minor Segment
In the figure, APB is the minor segment and AQB 
is the major segment
To find area of the minor segment APB, join the 
centre O to A and B.
Let <AOB = T
Area of minor segment APB
? = Area of sector OAPB — Area of ? OAB
? = ?pr²  - Area of ? OAB
360°
Page 5


? You know that area of a circle of radius r is pr
2
.
? You can imagine the circular region formed by the circle 
of radius r as a sector of angle 360
o
(Because angle at the 
centre is a complete angle).
? With this assumption, we can calculate the area of the 
sector OAPB as follows:
? Area of a sector of angle 360
o
= pr
2
? So, area of a sector of angle 1
o
= pr
2
360
o
? Hence, area of a sector of angle  = pr
2 
× ?
360°
=   pr
2
?
36o°
? Length of the Arc of a sector 
You know that circumference of a circle of radius r 
is 2 pr.
You can calculate the length of the arc of sector 
OAPB as follows:
Length of the arc of a sector of angle 360
o
= 2 pr
So, length of the arc of a sector of angle 1
o
= 2 pr
360
o
Hence, length of the arc of a sector of angle ? = 
?
360
×2 pr
?Recall that a chord of a circle divides the 
circular region into two parts. Each part is 
called a segment of the circle.
?There are two parts of area of segment :-
?Major Segment
?Minor Segment
In the figure, APB is the minor segment and AQB 
is the major segment
To find area of the minor segment APB, join the 
centre O to A and B.
Let <AOB = T
Area of minor segment APB
? = Area of sector OAPB — Area of ? OAB
? = ?pr²  - Area of ? OAB
360°
Major Segment
? = Area of sector OAQB + area of ? OAB
? pr²(360°- T) + Area of  ? AOB
360°
? Alternatively
? Area of major segment AQB
= Area of circle with centre O - Area of minor 
segment APB.