NCERT Class 10 Maths Chapter 11: Complete Resource for Areas Related to Circles
NCERT Solutions for Class 10 Maths Chapter 11 Areas Related To Circles
FAQs on NCERT Solutions for Class 10 Maths Chapter 11 Areas Related To Circles
1. What topics are covered in NCERT Solutions for Class 10 Maths Chapter 11: Areas Related to Circles?
The NCERT Solutions for Class 10 Maths Chapter 11 cover:
- Understanding the area and perimeter (circumference) of a circle
- Area and length formulas of sectors and segments of a circle
- Real-life problems involving areas of circular shapes and their combinations
- Use of CBSE-prescribed formulas for calculating areas enclosed by chords, arcs, and sectors
- Practice exercise for mastering application-based questions
2. How should students approach solving NCERT exercise 11.1 in Class 10 Maths Areas Related to Circles?
Students should solve Exercise 11.1 by:
- Reading each question carefully and identifying whether it deals with a circle, sector, or segment
- Listing given values (radius, angle, circumference, etc.)
- Selecting and applying the correct formula as per CBSE NCERT guidelines (e.g., Area of sector = (θ/360) × πr²)
- Showing step-by-step calculations for all sub-parts
- Reviewing diagrams and making rough sketches for clarity
3. What are the essential formulas used in Class 10 Maths Chapter 11 NCERT Solutions?
Key formulas include:
- Area of a circle: A = πr²
- Circumference: C = 2πr
- Length of arc: (θ/360) × 2πr
- Area of sector: (θ/360) × πr²
- Area of segment: Area of sector − Area of triangle formed by radii and chord
4. How many exercises and questions are there in NCERT Class 10 Maths Chapter 11 Areas Related to Circles (as per CBSE 2025–26)?
There is one exercise (Exercise 11.1) in Chapter 11 Areas Related to Circles, with fourteen solved questions provided in the NCERT Solutions. This streamlined format matches the latest CBSE 2025–26 syllabus update.
5. What is the advantage of using Vedantu’s NCERT Solutions for Class 10 Maths Chapter 11?
Vedantu’s NCERT Solutions provide:
- Stepwise explanations for all exercise questions
- CBSE exam-style solutions for clarity and accuracy
- Detailed diagrams and formula applications for tricky parts (like sectors and segments)
- Support for self-study and revision, especially before board exams
- Accessible explanations matching the latest NCERT and CBSE (2025–26) requirements
6. Can you explain the difference between a sector and a segment of a circle for Class 10 Maths?
A sector is the region between two radii and the connecting arc, resembling a ‘slice’ of the circle. A segment, in contrast, is the area between a chord and the arc lying between the chord's endpoints (excluding the centre). Segments are further classified as minor (smaller area) or major (larger area) based on their size.
7. What is the most common mistake students make when solving area-related questions on circles in Class 10 NCERT?
The most common mistake is using the wrong formula or unit. For example, students may:
- Confuse area of sector and length of arc
- Miscalculate angles (mixing degrees and radians)
- Use the wrong value for π (use the value specified in the problem)
- Forget to subtract the triangle’s area when calculating segment area
8. How do you find the area of a segment in Class 10 Maths Chapter 11 problems?
To find the area of a segment:
- First, calculate the area of the sector defined by the given angle and radius using (θ/360) × πr²
- Next, calculate the area of the triangle formed by the two radii and the chord (often using trigonometry or the formula for equilateral triangle when angles are 60° or 120°, as in NCERT)
- Subtract the area of the triangle from the sector to get the segment’s area
9. What are the real-life applications of areas related to circles as per the Class 10 syllabus?
Real-life applications include:
- Calculating areas and perimeters of circular objects, such as wheels, clocks, gardens, and pizzas
- Determining pathways and boundaries involving arcs or circles
- Designing circular segments for engineering or construction (e.g., brooch designs, road warning signals, umbrella ribs)
10. Why is it important to master CBSE Class 10 Maths Chapter 11 before board exams?
This chapter tests your understanding of geometry, formulas, and problem-solving, and is often a source of application-based or HOTS (Higher-Order Thinking Skills) questions in the board exam. Securing marks here boosts overall maths scores, and concepts from this chapter reappear in higher-level studies and competitive exams.
11. How can I quickly revise important formulas for areas related to circles for Class 10 boards?
Prepare a dedicated notebook page for:
- Area of circle (πr²)
- Circumference (2πr)
- Length of arc ((θ/360) × 2πr)
- Area of sector ((θ/360) × πr²)
- Area of segment (area of sector – area of triangle)
12. What is the formula for the area of a sector in Class 10 according to CBSE 2025–26 guidelines?
The area of a sector with central angle θ (in degrees) and radius r is calculated as: Area = (θ/360) × πr². Always use the value of π specified in the exam question (3.14 or 22/7).
13. If the CBSE board asks for the area of a major segment, what is the correct approach using NCERT Solutions?
To find the area of a major segment:
- Calculate the total area of the circle (πr²)
- Find the area of the minor segment (sector area – triangle area)
- Subtract the minor segment’s area from the total circle area to get the major segment’s area
14. How does the deleted syllabus for CBSE 2025–26 affect NCERT Solutions for Chapter 11: Areas Related to Circles?
As per CBSE 2025–26, the following topics are deleted from Chapter 11:
- Introduction to Area Related to Circles
- Perimeter and Area of a Circle - A Review
- Areas of combinations of Plane figures
15. What higher-order thinking skills (HOTS) questions can be asked from NCERT Solutions for Class 10 Maths Chapter 11?
HOTS questions can ask:
- Comparison of two areas formed by different segments or sectors
- Calculation of area left after removing a sector from a square or rectangle
- Problems involving rates of change (e.g., how area changes as radius increases)
- Design-based tasks (e.g., creating patterns using segments)

















