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Areas Related to Circles Class 10th Notes - Free NCERT Class 10 Maths Chapter 12 Notes - Download PDF

Areas Related to Circles Class 10th Notes - Free NCERT Class 10 Maths Chapter 12 Notes - Download PDF

Edited By Ramraj Saini | Updated on Apr 11, 2025 12:25 PM IST

The understanding of area related to circle properties forms the foundation to solve practical problems about area calculations and perimeter measurements, and sector subdivisions. The chapter presents procedures to find the circumference and area of circles, along with their sector and segment applications in daily scenarios. Students must practice all the topics of Trigonometry and their examples from the NCERT Exemplar Solutions for Class 10 Maths Chapter 11 Area related to circles. Students must practice questions and check solutions from the NCERT Solutions for Class 10 Maths Chapter 11 Area related to circles.

This Story also Contains
  1. NCERT notes Class 10 Maths Chapter 11 Areas Related to Circles
  2. Area of Circle:
  3. Circumference of Circle:
  4. Sector:
  5. Segment:
  6. Class 10 Chapter Wise Notes
Areas Related to Circles Class 10th Notes - Free NCERT Class 10 Maths Chapter 12 Notes - Download PDF
Areas Related to Circles Class 10th Notes - Free NCERT Class 10 Maths Chapter 12 Notes - Download PDF

NCERT notes Class 10 Maths Chapter 11 Areas Related to Circles

Area of Circle:

A circle's area denotes the complete space located between its defining boundaries.

To calculate the Area of a Circle, the formula is:

Area = πr2

(where r is radius)

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For Example, find the area of a circle with a radius of 14 cm.

Area of a circle = πr2 = 227 × 14 × 14 = 616 cm2

Circumference of Circle:

A circle's circumference represents the complete length of its boundary line. It is also known as the perimeter of the circle.

To calculate the Circumference of a Circle, the formula is:

Circumference = 2πr
(where r is radius)

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For Example, find the circumference of a circle with a radius of 14 cm.

Circumference of a Circle = 2πr = 2 × 227 × 14 = 88 cm.

Sector:

The portion (or part) of the circular region enclosed by two radii and the corresponding arc is called a sector of the circle.

Types of Sectors:

Minor Sector: If the minor arc of the circle forms part of the sector's boundary, it is called a minor sector, which means the smaller area of the circle enclosed by two radii.

Major Sector: If the major arc of the circle is part of the sector's boundaries, it is called a major sector, which means the larger area of the circle enclosed by two radii.


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Angle of a Sector:

The angle of a sector emerges as the central angle which forms between the two radii within the sector and extends from the circle center. The size of the sector depends on its central angle and is measured in degrees (°) or radians. Θ shown in the upper figure is the angle of a sector.

Area of a Sector of a Circle:

The area of the sector equates to the region that the sector occupies within the circle boundaries. A sector takes up part of the circle's overall space.
To calculate the Area of a sector of a Circle, the formula is:

Area = Θ360×πr2

(where Θ is angle of the sector and r is radius)

For Example, find the area of the sector if the angle of the sector is 90° and the radius of the circle is 14 cm.

Area of the sector = Θ360×πr2 = 90360×227×142

= 14 × 22 × 14 × 2 = 154 cm2

Length of an Arc of a Sector:

The curved sector boundary, which is a component of the circle's circumference, is known as the arc length.

To calculate the Area of a sector of a Circle, the formula is:

Length of an Arc = Θ360×2πr

(where Θ is angle of the sector and r is radius)

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For Example, find the length of the sector if the angle of the sector is 90° and the radius of the circle is 14 cm.

Length of the sector = Θ360 × 2πr = 90360 × 2 × 227 × 14

= 14 × 2 × 22 × 2 = 22 cm2

Segment:

The area of a circle that is bounded by a chord and its matching arc is called a segment. The center is not included.

Types of Segments:

Minor Segment: The smaller region of the circle cut off by the chord.

Major Segment: The larger region of the circle cut off by the chord.

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Area of Segment:

To calculate the Area of a segment of a Circle, the formula is:

Area of segment of a circle = Area of the corresponding sector – Area of the corresponding triangle.

For Example, A circle has a radius of 14 cm, and a chord subtends a 90° angle at the center. Find the area of the minor segment of the circle.

First, calculate the area of the sector:

Area of sector = Θ360×πr2 = 90360×227×142

= 14 × 22 × 14 × 2 = 154 cm2

Now, calculate the area of the triangle:

Since the angle is 90°, the triangle formed is a right-angled triangle with base and height equal to the radius (14 cm each). The formula for the area of a triangle is:

Area = 12 × base × height

So, area = 12 × 14 × 14 = 98 cm2

Area of the minor segment = Area of sector - Area of Triangle

So, Area of the minor segment = 154 - 98 = 56 cm2

Class 10 Chapter Wise Notes

Students must download the notes below for each chapter to ace the topics.


NCERT Notes For Class 10

The notes are written in a way that they align with the board exam pattern. The class 10 NCERT notes offer point-wise explanations of textbook chapters, highlight important terms and provide a focused preparation for the board exams.

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NCERT Exemplar Solutions for Class 10

Students must check the NCERT Exemplar solutions for class 10 of Mathematics and Science Subjects.

NCERT Solutions for Class 10

Students must check the NCERT solutions for class 10 of Mathematics and Science Subjects.

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NCERT Books and Syllabus

To learn about the NCERT books and syllabus, read the following articles and get a direct link to download them.

Download NCERT Notes for CBSE Class 9 to 12:

NCERT Notes


Frequently Asked Questions (FAQs)

1. What is the Formula for the Area of a Circle?

The circle's area denotes the complete space located between its defining boundaries.

To calculate the Area of a Circle, the formula is: 

Area = πr2
(where r is radius)

2. How Do You Calculate the Circumference of a Circle?

A circle's circumference represents the complete length of its boundary line. It is also known as the perimeter of the circle. 

To calculate the Circumference of a Circle, the formula is: 

Circumference = 2πr
(where r is radius)

3. How Do You Find the Area of a Sector of a Circle?

The area of the sector equates to the region that the sector occupies within the circle boundaries. A sector takes up part of the circle's overall space.

To calculate the Area of a sector of a Circle, the formula is: 

Area = Θ360×πr2
(where Θ is angle of the sector and r is radius)

4. What is the Formula for the Length of an Arc of a Circle?

The curved sector boundary, which is a component of the circle's circumference, is known as the arc length.

To calculate the Area of a sector of a Circle, the formula is:

Length of an Arc = Θ360×2πr
(where Θ is angle of the sector and r is radius)

5. How Do You Find the Area of a Segment of a Circle?

The area of a circle that is bounded by a chord and its matching arc is called a segment. The center is not included.

To calculate the Area of a segment of a Circle, the formula is:

Area of segment of a circle = Area of the corresponding sector – Area of the corresponding triangle.

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Option 1)

0.34\; J

Option 2)

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2,000 \; J - 5,000\; J

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20,000 \, \, J - 50,000 \, \, J

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K/2\,

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Option 1)

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Option 2)

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67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

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0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

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If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

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increase two fold

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less than 3

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