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Areas Related to Circles Class 10 PPT

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 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.
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120 videos|463 docs|105 tests

FAQs on Areas Related to Circles Class 10 PPT

1. What is the formula to find the circumference of a circle?
Ans. The formula to find the circumference of a circle is C = 2πr, where "C" represents the circumference and "r" represents the radius of the circle.
2. How can we find the area of a sector of a circle?
Ans. To find the area of a sector of a circle, we can use the formula A = (θ/360)πr^2, where "A" represents the area, "θ" represents the central angle of the sector in degrees, and "r" represents the radius of the circle.
3. What is the relationship between the diameter and the radius of a circle?
Ans. The diameter of a circle is twice the length of its radius. In other words, the diameter is equal to 2 times the radius.
4. How can we find the length of an arc of a circle?
Ans. To find the length of an arc of a circle, we can use the formula L = (θ/360)2πr, where "L" represents the length, "θ" represents the central angle of the arc in degrees, and "r" represents the radius of the circle.
5. What is the relationship between the circumference and the diameter of a circle?
Ans. The circumference of a circle is equal to π times the diameter of the circle. In other words, the circumference is equal to πd, where "d" represents the diameter.
120 videos|463 docs|105 tests
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