Chapter Notes: Area Related to Circles

# Area Related to Circles Chapter Notes - Mathematics (Maths) Class 10

## Area of Sector

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 = πr2
Using Unitary Method
Area represented by 360° = πr2
Area represented by

### Area of Semi Circle

Semi-Circle is a sector forming an angle 180° with center.
θ=180°
Now, Area of Semi Circle will be given as

Area of the Semi-Circle = πr2/2

### Area of Quarter Circle

Now, Area of Quarter Circle will be given as

Area of Quarter Circle =πr2/4

### Area of Segment

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

### Perimeter of Sector

• It is the length which enclosed the sector.
• Length of arc AB + OA + OB.
• OA=OB=r, that is radius of sector.

So,

perimeter of a Sector = l + 2r
Here l is length of arc and

The document Area Related to Circles Chapter Notes | Mathematics (Maths) Class 10 is a part of the Class 10 Course Mathematics (Maths) Class 10.
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## Mathematics (Maths) Class 10

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## FAQs on Area Related to Circles Chapter Notes - Mathematics (Maths) Class 10

 1. What is the formula for finding the area of a sector?
Ans. The formula for finding the area of a sector is (θ/360) * π * r², where θ is the angle of the sector in degrees and r is the radius of the circle.
 2. How do you find the angle of a sector if the area is given?
Ans. To find the angle of a sector when the area is given, first calculate the whole area of the circle using the formula A = π * r². Then, use the formula θ = (Area/A) * 360, where θ is the angle of the sector and A is the given area.
 3. Can the area of a sector be greater than the area of the whole circle?
Ans. No, the area of a sector cannot be greater than the area of the whole circle. The area of the whole circle is the maximum area that can be enclosed within its circumference. A sector is a part of the circle, so its area will always be less than or equal to the area of the whole circle.
 4. How do you find the length of the arc of a sector?
Ans. To find the length of the arc of a sector, you can use the formula (θ/360) * 2 * π * r, where θ is the angle of the sector in degrees and r is the radius of the circle.
 5. Can the angle of a sector be greater than 360 degrees?
Ans. No, the angle of a sector cannot be greater than 360 degrees. A circle has a total of 360 degrees, so any sector within the circle will have an angle less than or equal to 360 degrees.

## Mathematics (Maths) Class 10

115 videos|478 docs|129 tests

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