Class 10th Math Areas Related to Circles NCERT Notes CBSE 2023
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Areas Related to Circles Class 10 Notes

Areas Related to Circles Class Notes

Chapter 12 Areas Related to Circles

Class 10 Areas of Circles Mathematics is an important chapter introducing the formulas and concepts for calculating the area of ​​a circle. This chapter is very important for students to learn and understand how formulas for calculating the area of ​​curved shapes are derived. To get a good grasp of these concepts, download the NCERT notes for Class 10 Circular Math Areas and get ready.

NCERT notes for class 10 math chapter 12 by Vidyakul experts are very accurate and precise. When students are exposed to standard CBSE questions, Vidyakul aims to simplify student preparation by providing free Chapter 12 math notes for 10th graders. Passing the CBSE Board exam with honors requires maximum concentration and practice. Using NCERT Book notes materials, students can enhance their learning and preparation methods.



MATHEMATICS NOTES CLASS 10th CH-12



Points to Remember

Some of the important points to remember from this chapter are as follows:


  • Area of a circle

”Area

Area of a circle is πr2, where π=22/7 or ≈ 3.14 (can be used interchangeably for problem-solving purposes) and r is the radius of the circle.

π is the ratio of the circumference of a circle to its diameter.


  • Circumference of a Circle

The circumference of a circle is the distance covered by going around its boundary once.

”Circumference

The perimeter of a circle has a special name: Circumference, which is π times the diameter which is given by the formula;

Circumference of a circle = 2πr.


  • Segment of a Circle

A circular segment is a region of a circle that is “cut off” from the rest of the circle by a secant or a chord.

”Segment


  • Sector of a Circle

A circle sector/ sector of a circle is defined as the region of a circle enclosed by an arc and two radii. The smaller area is called the minor sector and the larger area is called the major sector.

”Sector


  • Angle of a Sector

The angle of a sector is the angle that is enclosed between the two radii of the sector.


  • Area of a Sector of a Circle

Area of a sector is given by

(θ/360°)×πr2

where ∠θ is the angle of this sector(minor sector in the following case) and r is its radius


  • Length of an arc of a sector

”Length

The length of the arc of a sector can be found by using the expression for the circumference of a circle and the angle of the sector, using the following formula:

L= (θ/360°)×2πr

Where θ is the angle of sector and r is the radius of the circle.


  • Area of a Triangle

The Area of a triangle is,

Area=(1/2)×base×height

If the triangle is an equilateral then

Area=(√3/4)×a2  where “a” is the side length of the triangle.









  • Area of a Segment of a Circle

Area related to circles class 10 -2

Area of segment APB (highlighted in yellow)

= (Area of sector OAPB) – (Area of triangle AOB)

=[(∅/360°)×πr2] – [(1/2)×AB×OM]

[To find the area of triangle AOB, use trigonometric ratios to find OM (height) and AB (base)]

Also, the Area of segment APB can be calculated directly if the angle of the sector is known using the following formula.

 =[(θ/360°)×πr2] – [r2×sin θ/2 × cosθ/2]

Where θ is the angle of the sector and r is the radius of the circle.


  • Formulas List

All these formulas are tabulated as given below for quick revision.

Parameters of Circles

Formulas

Area of the sector of angle θ

(θ/360°) × πr2

Length of an arc of a sector of angle θ

(θ/360°) × 2πr

Area of major sector 

πr2 – (θ/360°) × πr2

Area of a segment of a circle

Area of the corresponding sector – Area of the corresponding triangle

Area of the major segment

πr2 – Area of segment (minor segment)



  • Areas of different plane figures

–    Area of a square (side l) =l2

–    Area of a rectangle =l×b, where l and b are the length and breadth of the rectangle

–    Area of a parallelogram =b×h, where “b” is the base and “h” is the perpendicular height.


Topics and Sub-topics

Vidyakul’s talented professionals are developing these notes to help students achieve better grades. Vidyakul also provides free NCERT examples and books. These study materials are very helpful in preparing for the exam.

Now, let us look at the important topics from this chapter:

Sr. No.

Topic Name

12.1

Area of a Circle

12.2

Circumference of a Circle

12.3

Segment of a Circle

12.4

Sector of a Circle

12.5

Angle of a Sector

 

12.6

Area of a Sector of a Circle

 

12.7

Length of an arc of a sector

 

12.8

Area of a Triangle

 

 

12.9

Area of a Segment of a Circle

 

12.10

Areas of different plane figures

 

12.11

Areas of Combination of Plane figures

 

 


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Areas Related to Circles Class 10 Maths Notes Part - 1

Areas Related to Circles Class 10 Maths Notes Part - 2