CBSE Class 10 Mathematics (Standard) Chapter 11 Areas Related to Circles Important Questions 2027
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17 questions from Areas Related to Circles appeared in 6 of the 7 CBSE papers we analysed (2022–2026) — here are the topics that matter, the questions that repeat, and every previous-year question from this chapter.
Key facts
- Mensuration unit — 10 marks in the official syllabus
- Asked in 6 of 7 analysed papers (2022–2026)
- About 2.4 questions per paper (OR alternatives counted separately)
- 2 question patterns repeated across papers
Important topics in Areas Related to Circles
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Area of sector and length of arc | Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 2 | Area of segment (60/90/120 degrees) | Board 2023Board 2024Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
Repeated questions from Areas Related to Circles
1. Segment area = sector minus triangle
5×Board 2023Board 2024Board 2026Sample 2025Sample 20261/2/3/5 marks
AB is a chord of a circle centred at O such that angle AOB = 60 deg. If OA = 14 cm then find the area of the minor segment. (take sqrt(3) = 1.73)
2. Sector area from radius and angle
2×Board 2025Board 20262/3 marks
Find the area of the sector of a circle of radius 42 cm and of central angle 30 degrees. Also, find the area of the corresponding major sector. [Use pi = 22/7]
Areas Related to Circles questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 0 | 0 |
| Board 2023 | 1 | 5 |
| Board 2024 | 1 | 5 |
| Board 2025 | 6 | 8 |
| Sample 2025 | 3 | 7 |
| Board 2026 | 2 | 4 |
| Sample 2026 | 4 | 6 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Areas Related to Circles
Board 2026 2 questions
Area of a segment of a circle of radius 'r' and central angle 60 degrees is : (A) (pi r2)/2 - (1/2) r2 (B) (2 pi r)/4 - (sqrt(3)/4) r2 (C) (pi r2)/6 - (sqrt(3)/4) r2 (D) (2 pi r)/4 - r2 sin 60
Find the area of the sector of a circle of radius 42 cm and of central angle 30 degrees. Also, find the area of the corresponding major sector. [Use pi = 22/7]
Sample 2026 4 questions
Given below is the picture of the Olympic rings made by taking five congruent circles of radius 1cm each, intersecting in such a way that the chord formed by joining the point of intersection of two circles is also of length 1cm. Total area of all the dotted regions (assuming the thickness of the rings to be negligible) is (A) 4[pi/12 - sqrt(3)/4] cm2 (B) [pi/6 - sqrt(3)/4] cm2 (C) 4[pi/6 - sqrt(3)/4] cm2 (D) 8[pi/6 - sqrt(3)/4] cm2. [For Visually Impaired candidates: The area of the circle that can be inscribed in a square of 6 cm is (A) 36pi cm2 (B) 18pi cm2 (C) 12pi cm2 (D) 9pi cm2]
The area (in cm2) of a sector of a circle of radius 21cm cut off by an arc of length 22cm is (A) 441 (B) 321 (C) 231 (D) 221
A horse, a cow and a goat are tied, each by ropes of length 14m, at the corners A, B and C respectively, of a grassy triangular field ABC with sides of lengths 35m, 40m and 50m. Find the area of grass field that can be grazed by them.
Find the area of the major segment (in terms of pi) of a circle of radius 5cm, formed by a chord subtending an angle of 90 degrees at the centre.
Board 2025 6 questions
If a sector of a circle has an area of 40*pi sq. units and a central angle of 72 deg, the radius of the circle is : (A) 200 units (B) 100 units (C) 20 units (D) 10*sqrt(2) units
A piece of wire 20 cm long is bent into the form of an arc of a circle of radius 60/pi cm. The angle subtended by the arc at the centre of the circle is : (A) 30 deg (B) 60 deg (C) 90 deg (D) 50 deg
[case context: circular silver-wire brooch of diameter 35 mm; wire also forms 5 diameters dividing the circle into 10 equal sectors] Find the central angle of each sector.
[case context: circular silver-wire brooch of diameter 35 mm; wire also forms 5 diameters dividing the circle into 10 equal sectors] Find the length of the arc ACB.
[case context: circular silver-wire brooch of diameter 35 mm; wire also forms 5 diameters dividing the circle into 10 equal sectors] Find the area of each sector of the brooch.
[case context: circular silver-wire brooch of diameter 35 mm; wire also forms 5 diameters dividing the circle into 10 equal sectors] Find the total length of the silver wire used.
Sample 2025 3 questions
Assertion (A): If the radius of sector of a circle is reduced to its half and angle is doubled then the perimeter of the sector remains the same. Reason (R): The length of the arc subtending angle theta at the centre of a circle of radius r = (pi*r*theta)/180. [Choose: A) Both A and R true, R correct explanation B) Both true, R not correct explanation C) A true, R false D) A false, R true]
The minute hand of a wall clock is 18 cm long. Find the area of the face of the clock described by the minute hand in 35 minutes.
AB is a chord of a circle centred at O such that angle AOB = 60 deg. If OA = 14 cm then find the area of the minor segment. (take sqrt(3) = 1.73)
Board 2024 1 question
An arc of a circle of radius 21 cm subtends an angle of 60 degrees at the centre. Find: (i) the length of the arc. (ii) the area of the minor segment of the circle made by the corresponding chord.
Board 2023 1 question
A chord of a circle of radius 14 cm subtends an angle of 60 degrees at the centre. Find the area of the corresponding minor segment of the circle. Also find the area of the major segment of the circle.
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Standard) Chapter 11 Areas Related to Circles?
By how often and how recently they were asked: Area of sector and length of arc; Area of segment (60/90/120 degrees).
How many marks does Areas Related to Circles carry in the CBSE Class 10 Mathematics (Standard) exam?
Areas Related to Circles is part of the Mensuration unit, which carries 10 marks in the official syllabus. In the analysed papers it had about 2.4 questions per paper.
Do questions from Areas Related to Circles repeat in board exams?
Yes — 2 question patterns from this chapter appeared in two or more past board or official sample papers. They are listed on this page with the years they were asked.