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 |
Being in CBSE class 10th and considering the board examinations you must be needing resources to excel in your examinations. At TestprepKart we take great pride in providing CBSE class 10th all study resources in downloadable form for you to keep you going.
Below is the list of all CBSE class 10th Downloads available on TestprepKart for both Indian and NRI students preparing for CBSE class 10th in UAE, Oman, Qatar, Kuwait & Bahrain.
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.
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