CBSE Class 10 Mathematics (Basic) 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)
- 3 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 2026 | ★★★☆☆ |
| 2 | Area of segment (60/90/120 degrees) | Board 2024Board 2025Board 2026Sample 2025 | ★☆☆☆☆ |
| 3 | Areas of combinations of plane figures | Board 2023 | ★☆☆☆☆ |
Repeated questions from Areas Related to Circles
1. Area of minor segment
3×Board 2024Board 2025Board 20262/5 marks
A chord of a circle of diameter 20 cm subtends an angle of 60° at the centre of the circle. Find the area of the corresponding minor segment of the circle. (Use π = 3.14 and √3 = 1.73)
2. Perimeter of shaded sector
2×Board 2025Board 20261 marks
The perimeter of the shaded region in the given figure is : [Circle with centre O; two radii r bounding a shaded sector, chord a subtending the sector, and arc l] (A) l (B) l + a (C) l + 2r (D) l + 2r + a
3. Ratio of quadrant to circle
2×Board 2025Board 20261 marks
The ratio of the area of a quadrant of a circle to the area of the same circle is : (A) 1 : 2 (B) 2 : 1 (C) 1 : 4 (D) 4 : 1
Areas Related to Circles questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 0 | 0 |
| Board 2023 | 4 | 6 |
| Board 2024 | 1 | 5 |
| Board 2025 | 3 | 4 |
| Sample 2025 | 1 | 5 |
| Board 2026 | 3 | 4 |
| Sample 2026 | 5 | 7 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Areas Related to Circles
Board 2026 3 questions
The perimeter of the shaded region in the given figure is : [Circle with centre O; two radii r bounding a shaded sector, chord a subtending the sector, and arc l] (A) l (B) l + a (C) l + 2r (D) l + 2r + a
The ratio of the area of a quadrant of a circle to the area of the same circle is : (A) 1 : 2 (B) 2 : 1 (C) 1 : 4 (D) 4 : 1
A chord of a circle of diameter 20 cm subtends an angle of 60° at the centre of the circle. Find the area of the corresponding minor segment of the circle. (Use π = 3.14 and √3 = 1.73)
Sample 2026 5 questions
The circumferences of two circles are in the ratio 3 : 4. The ratio of their areas is
A) 3 : 4
B) 4 : 3
C) 9 : 16
D) 16 : 9
[Water sprinkler shoots a stream of water a distance of 21 m and rotates through an angle equal to the complementary angle of 10°, watering a sector-shaped region.] What is the area of sector in terms of arc length?
[Water sprinkler shoots a stream of water a distance of 21 m and rotates through an angle equal to the complementary angle of 10°, watering a sector-shaped region.] What is the area of the watered region (in terms of π)?
[Water sprinkler shoots a stream of water a distance of 21 m and rotates through an angle equal to the complementary angle of 10°, watering a sector-shaped region.] If the radius (r) changes to 28 m, find the angle θ so that the area of the watered region remains the same.
[Water sprinkler shoots a stream of water a distance of 21 m and rotates through an angle equal to the complementary angle of 10°, watering a sector-shaped region.] If the radius (r) is increased from 21 m to 28 m and the angle remains the same, what is the increase in the area of the watered region?
Board 2025 3 questions
The perimeter of the shaded region in the given figure is : (sector of a circle, centre O, two radii r, chord a, arc length l) (A) l (B) l + a (C) l + 2r (D) l + 2r + a
The ratio of the area of a quadrant of a circle to the area of the same circle is : (A) 1 : 2 (B) 2 : 1 (C) 1 : 4 (D) 4 : 1
A chord of a circle of diameter 20 cm subtends an angle of 60° at the centre of the circle. Find the area of the corresponding minor segment of the circle. (Use π = 3.14 and √3 = 1.73)
Sample 2025 1 question
The perimeter of sector OACB of the circle centred at O and of radius 24, is 73.12 cm. (i) Find the central angle ∠AOB. (ii) Find the area of the minor segment ACB. (Use π = 3.14 and √3 = 1.73)
Board 2024 1 question
A chord of a circle of radius 14 cm subtends an angle of 90° at the centre. Find the area of the corresponding minor and major segments of the circle.
Board 2023 4 questions
[Case: A Rangoli is in the shape of square ABCD of side 40 cm; at each corner a quadrant of a circle of radius 10 cm is drawn, and a circle of diameter 20 cm is drawn inside the square.] What is the area of square ABCD ?
[Case: A Rangoli is in the shape of square ABCD of side 40 cm; at each corner a quadrant of a circle of radius 10 cm is drawn, and a circle of diameter 20 cm is drawn inside the square.] Find the area of the circle.
[Case: A Rangoli is in the shape of square ABCD of side 40 cm; at each corner a quadrant of a circle of radius 10 cm is drawn, and a circle of diameter 20 cm is drawn inside the square.] If the circle and the four quadrants are cut off from the square ABCD and removed, then find the area of remaining portion of square ABCD.
[Case: A Rangoli is in the shape of square ABCD of side 40 cm; at each corner a quadrant of a circle of radius 10 cm is drawn, and a circle of diameter 20 cm is drawn inside the square.] Find the combined area of 4 quadrants and the circle, removed.
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Basic) 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); Areas of combinations of plane figures.
How many marks does Areas Related to Circles carry in the CBSE Class 10 Mathematics (Basic) 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 — 3 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.