NCERT Solutions Class 10 Maths Chapter 12 helps you calculate areas and perimeters of circles, sectors, and segments with precision. You’ll learn how to apply formulas for finding the area of combinations of plane figures, solve problems involving circular tracks and designs, and master the relationship between arc length, central angle, and radius. These practical skills are essential for solving real-world geometry problems and scoring well in board exams.
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All exercises with step-by-step solutions | Updated 2025-26 | Free Download
Download PDF (Free)NCERT Solutions Class 10 Maths Chapter 12 Areas Related to Circles – Complete Guide
NCERT Class 10 Chapter 12 – Areas Related to Circles is a fundamental chapter that builds upon your knowledge of circles from previous classes. You’ll explore various aspects of circular regions including the area and circumference of complete circles, sectors (pie-shaped portions), and segments (regions between chords and arcs). This chapter carries 5 marks weightage in your CBSE board examination and typically includes 2-3 questions ranging from 2 to 4 marks each.
📊 CBSE Class 10 Maths Chapter 12 – Exam Weightage & Marking Scheme
| CBSE Board Marks | 5 Marks |
| Unit Name | Mensuration |
| Difficulty Level | Medium |
| Importance | Medium |
| Exam Types | CBSE Board, State Boards |
| Typical Questions | 1-2 questions |
You will learn to apply formulas for calculating areas and perimeters of sectors and segments, understanding the relationship between central angles and arc lengths. The chapter emphasizes problem-solving with combinations of plane figures, where circles interact with triangles, rectangles, and squares. You’ll encounter questions involving circular paths, running tracks, flower beds, and designs that combine multiple geometric shapes – all common scenarios in CBSE board exams.
This chapter has excellent practical applications in architecture, engineering, and everyday life. Whether it’s calculating the area of a pizza slice, designing circular gardens, or determining material needed for circular decorations, these concepts are highly relevant. The mathematical skills you develop here also form the foundation for mensuration topics in higher classes and competitive examinations.
Quick Facts – Class 10 Chapter 12
| 📖 Chapter Number | Chapter 12 |
| 📚 Chapter Name | Areas Related to Circles |
| ✏️ Total Exercises | 2 Exercises |
| ❓ Total Questions | 17 Questions |
| 📅 Updated For | CBSE Session 2025-26 |
Mastering Areas Related to Circles requires understanding the derivations of formulas and practicing diverse problem types. Focus on MCQs for quick concept checks, short answer questions (2-3 marks) for formula applications, and long answer questions (4 marks) for complex combinations. With consistent practice using NCERT solutions and previous year CBSE papers, you’ll confidently tackle any question from this moderately difficult yet scoring chapter.
NCERT Solutions Class 10 Maths Chapter 12 – All Exercises PDF Download
Download exercise-wise NCERT Solutions PDFs for offline study
| Exercise No. | Topics Covered | Download PDF |
|---|---|---|
| Exercise 12.1 | Complete step-by-step solutions for 9 questions | 📥 Download PDF |
| Exercise 12.2 | Complete step-by-step solutions for 8 questions | 📥 Download PDF |
Areas Related to Circles – Key Formulas & Concepts
Quick reference for CBSE exams
| Formula | Description | When to Use |
|---|---|---|
| Area of a Circle \(\pi r^2\) | Calculates the area enclosed by a circle. Note: Remember to use the correct value of \(\pi\) (either 22/7 or 3.14, as specified in the question). | Finding the area of circular regions, calculating the area of shaded regions involving circles. |
| Circumference of a Circle \(2 \pi r\) | Calculates the length of the boundary of a circle. Note: Also known as the perimeter of the circle. | Finding the length of a circular track, calculating the distance covered in a certain number of revolutions. |
| Area of a Sector \(\frac{\theta}{360} \times \pi r^2\) | Calculates the area of a sector of a circle, where \(\theta\) is the angle subtended by the arc at the center. Note: \(\theta\) must be in degrees. Make sure you are using the correct angle of the sector. | Finding the area of a ‘slice’ of a circle. Problems involving clock hands or pizza slices. |
| Length of an Arc \(\frac{\theta}{360} \times 2 \pi r\) | Calculates the length of the arc of a sector, where \(\theta\) is the angle subtended by the arc at the center. Note: \(\theta\) must be in degrees. This is a fraction of the total circumference. | Finding the length of the curved boundary of a sector. Problems involving the distance an object travels along a circular path. |
| Area of a Segment Area of Sector – Area of Corresponding Triangle | Calculates the area of a segment (region between a chord and the arc). Note: You may need to use trigonometry to find the area of the triangle if it’s not right-angled. Common case: equilateral triangle. | Finding the area of a ‘slice’ of a circle with a straight edge cut off. |
| Area of Equilateral Triangle (within a segment) \(\frac{\sqrt{3}}{4} a^2\) | Area of an equilateral triangle where ‘a’ is the side length. Note: Remember to use the same units for ‘a’ as for the radius of the circle. | When the triangle formed in the segment is equilateral (often when central angle is 60 or 120 degrees) |
| Area of a Semicircle \(\frac{1}{2} \pi r^2\) | Calculates the area of half a circle. Note: It’s half the area of a full circle. | Finding the area of regions made of semicircles, or when a circle is bisected. |
| Perimeter of a Semicircle \(\pi r + 2r\) | Calculates the total length of the boundary of a semicircle (arc + diameter). Note: Includes both the curved arc and the diameter. | Finding the perimeter of semi-circular regions. Be careful not to only use \(\pi r\). |
| Area of a Quadrant \(\frac{1}{4} \pi r^2\) | Calculates the area of one-fourth of a circle. Note: A sector with a central angle of 90 degrees. | When dealing with regions that are exactly 1/4 of a circle, often in squares or rectangles. |
| Relationship between Arc Length, Radius and Angle \(l = r \theta\) | Relates the arc length (\(l\)), radius (\(r\)), and central angle (\(\theta\)) in radians. Note: Ensure \(\theta\) is in radians. To convert degrees to radians: \(\text{radians} = \frac{\pi}{180} \times \text{degrees}\) | When the angle is given in radians, this is a direct formula to calculate arc length. |
Frequently Asked Questions – NCERT Class 10 Maths Chapter 12
📚 Related Study Materials – Class 10 Maths Resources
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| NCERT Class 10 Maths All Chapters | View Solutions |
| NCERT Class 10 Science Solutions | View Solutions |
| NCERT Class 10 Social Science | View Solutions |
| NCERT Class 10 English Solutions | View Solutions |