# CBSE Class 10th Areas Related to Circles Details & Preparations Downloads

In the expansive realm of Class 10 mathematics, the chapter on "Areas Related to Circles" emerges as a pivotal exploration. This topic goes beyond the conventional study of circles, delving into the intricate relationships between geometric figures and their areas. Join us on a journey through the mathematical landscape where circles intersect with sectors, segments, and more.

**Unlocking Geometric Insights: CBSE NCERT Download Demystifies 'Areas Related to Circles' in Class 10 Mathematics**

**Area of a Circle**

The 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.

Example: Find the area of a circle with radius = 7cm.

Solution: Given, radius of circle = 7cm

By the formula we know;

Area of circle = πr2

= π(7)2

= (22/7) (7)2

= 154 sq.cm.

**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.

Example: The circumference of a circle whose radius is 21cm is given by;

C = 2πr

= 2 (22/7) (21)

= 132 cm

**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

The area of a sector is given by (θ/360°)×πr2

**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]

**CBSE Class 10 NCERT Mathematics Topics for a Strong Foundation (NCERT DOWNLOAD)**

Chapter Name |
Areas Related to Circles |

Topic Number |
Topics |

11.1 |
Areas of Sector and Segment of a Circle |

11.2 |
Summary |

**I. Circle Basics: A Recap of the Essentials**

Before we dive into the complexities, let's revisit the fundamentals of circles. Understanding concepts like radius, diameter, and circumference provides a solid foundation for exploring the nuanced relationships in the upcoming sections.

**II. Areas of Circles: The Heart of the Matter**

The blog delves into the calculation of the area of a circle, unraveling the formula and its applications. Students discover how this fundamental concept lays the groundwork for exploring more advanced topics related to circular areas.

**III. Sectors and Arcs: Exploring Proportions**

As we progress, the focus shifts to sectors and arcs. Students explore the relationships between angles, arc lengths, and sector areas, unraveling the proportionalities that govern these interconnected elements within a circle.

**IV. Segments: Dividing Circles with Precision**

The exploration extends to circle segments, where students learn to calculate the area of the region between a chord and its corresponding arc. This concept adds another layer of complexity, enhancing students' geometric problem-solving skills.

**V. Composite Figures: Integrating Geometric Elements**

The blog concludes by tackling composite figures formed by combining different geometric elements within a circle. This section challenges students to apply their knowledge to solve problems involving intricate shapes, further honing their analytical abilities.

**CBSE Class 10 Board Exam Sample Paper**

**[Previous Year Question Solution Maths Download Button]
[Previous Year Question Solution Science Download Button]**

CBSE CLASS 10 Mathematics Chapters |

Chapter1: Real Numbers |

Chapter2: Polynomials |

Chapter3: Pair of Linear Equations in Two Variables |

Chapter4: Quadratic Equations |

Chapter5: Arithmetic Progressions |

Chapter6: Triangles |

Chapter7: Coordinate Geometry |

Chapter8: Introduction to Trigonometry |

Chapter9: Some Applications of Trigonometry |

Chapter10: Circles |

Chapter11: Areas Related to Circles |

Chapter12: Surface Areas and Volumes |

Chapter13: Statistics |

Chapter14: Probability |

CBSE CLASS 10 Science Chapters |

Chapter1: Chemical Reactions and Equations |

Chapter2: Acids, Bases and Salts |

Chapter3: Metals and Non-metals |

Chapter4: Carbon and its Compounds |

Chapter5: Life Processes |

Chapter6: Control and Coordination |

Chapter7: How do Organisms Reproduce? |

Chapter8: Heredity |

Chapter9: Light – Reflection and Refraction |

Chapter10: The Human Eye and the Colourful World |

Chapter11: Electricity |

Chapter12: Magnetic Effects of Electric Current |

Chapter13: Our Environment |

Class 8 |

Class 9 |

Class 11 |

Class 12 |

**CBSE Class 10th Downloadable Resources: **

1. CBSE Class 10th Topic Wise Summary | View Page / Download |

2. CBSE Class 10th NCERT Books | View Page / Download |

3. CBSE Class 10th NCERT Solutions | View Page / Download |

4. CBSE Class 10th Exemplar | View Page / Download |

5. CBSE Class 10th Previous Year Papers | View Page / Download |

6. CBSE Class 10th Sample Papers | View Page / Download |

7. CBSE Class 10th Question Bank | View Page / Download |

8. CBSE Class 10th Topic Wise Revision Notes | View Page / Download |

9. CBSE Class 10th Last Minutes Preparation Resources (LMP) | View Page / Download |

10. CBSE Class 10th Best Reference Books | View Page / Download |

11. CBSE Class 10th Formula Booklet | View Page / Download |

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**FAQ**

**Q1: What is the formula for calculating the area of a circle?**

**Ans** The formula for the area of a circle is \( \pi r^2 \), where \( r \) is the radius of the circle.

**Q2: How do you find the area of a sector in a circle?**

**Ans ** To find the area of a sector, use the formula \( \frac{\theta}{360} \times \pi r^2 \), where \( \theta \) is the central angle in degrees.

**Q3: What is the difference between an arc and a sector in a circle?**

**Ans **An arc is a portion of the circle's circumference, while a sector is the region enclosed by an arc and the two radii connecting its endpoints to the center.

**Q4: Can you explain the concept of a chord in a circle?
Ans** A chord is a straight line segment connecting two points on the circle. The diameter is a special type of chord that passes through the center.

**Q5: How is the area of a circle related to its circumference?
Ans** The circumference (C) of a circle is related to its area (A) through the formula \( C = 2\pi r \), where \( r \) is the radius.