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 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.

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.

• 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.

• 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

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 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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