Areas Related to Circles: CBSE Class 10 Previous Year Questions

127 different questions from Areas Related to Circles (NCERT Chapter 11) asked in CBSE Class 10 Maths board exams 2022–2026. Pick a mark group to practise, each with answers and step-by-step solutions.

1 mark questions63 questions 2 marks questions12 questions 3 marks questions30 questions 4 marks questions13 questions 5 marks questions9 questions

Most asked Areas Related to Circles questions

Q171 markMCQAreas Related to Circles CBSE 2026 · Basic 430/5/1

The length of a pendulum is 70 cm and it describes an arc of length 88 cm when swings. The angle subtended by the arc at the centre is

(A) $3 6^{\circ}$
(B) $7 0^{\circ}$
(C) $7 2^{\circ}$
(D) $8 0^{\circ}$

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Answer: (C)

7 2^{\circ}

Arc length $= \frac{θ}{36 0 ^{\circ}} \times 2 π r$
$88 = \frac{θ}{36 0 ^{\circ}} \times 2 \times \frac{22}{7} \times 70 = \frac{θ}{36 0 ^{\circ}} \times 440$
$θ = \frac{88 \times 36 0 ^{\circ}}{440} = 7 2^{\circ}$

Also asked in: 2026 Basic 430/5/2, 2026 Basic 430/5/3

Q171 markMCQAreas Related to Circles CBSE 2026 · Standard 30/4/1

Arc PQ subtends an angle $θ$ at the centre of the circle with radius 6.3 cm. If $P Q ⌢ = 11$ cm, then the value of $θ$ is

(A) $1 0^{\circ}$
(B) $6 0^{\circ}$
(C) $4 5^{\circ}$
(D) $10 0^{\circ}$

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Answer: (D)

10 0^{\circ}

Arc length $= \frac{θ}{36 0 ^{\circ}} \times 2 π r$
$11 = \frac{θ}{36 0 ^{\circ}} \times 2 \times \frac{22}{7} \times 6.3 = \frac{θ}{36 0 ^{\circ}} \times 39.6$
$θ = \frac{11 \times 36 0 ^{\circ}}{39.6} = 10 0^{\circ}$

Also asked in: 2026 Standard 30/4/2, 2026 Standard 30/4/3

Q313 marksShort AnswerAreas Related to Circles CBSE 2026 · Basic 430/5/1

Chord AB of a circle subtends an angle of $12 0^{\circ}$ at the centre O of the circle. Find the length of arc AB, if radius of the circle is 21 cm.

Diagram for CBSE 2026 Class 10 Maths question 31

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Answer: 44 cm

Arc length $= \frac{θ}{36 0 ^{\circ}} \times 2 π r = \frac{12 0 ^{\circ}}{36 0 ^{\circ}} \times 2 \times \frac{22}{7} \times 21$
$= \frac{1}{3} \times 132 = 44$ cm

Also asked in: 2026 Basic 430/5/2, 2026 Basic 430/5/3

Q273 marksShort AnswerAreas Related to Circles CBSE 2026 · Standard 30/3/1

In the given figure, chord AB subtends an angle of $12 0^{\circ}$ at the centre of the circle with radius 7 cm. Find (i) perimeter of major sector OACB, and (ii) area of the shaded segment, if area of $Δ$ OAB = 21.2 cm $^{2}$ .

Diagram for CBSE 2026 Class 10 Maths question 27

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Answer: (i)

\frac{130}{3} \approx 43.33

cm (ii)

\approx 30.13

^{2}

(i) Major sector angle $= 36 0^{\circ} - 12 0^{\circ} = 24 0^{\circ}$
Arc ACB $= \frac{240}{360} \times 2 \times \frac{22}{7} \times 7 = \frac{88}{3}$ cm
Perimeter $= 7 + 7 + \frac{88}{3} = \frac{130}{3} \approx 43.33$ cm
(ii) Area of minor sector OAB $= \frac{120}{360} \times \frac{22}{7} \times 7^{2} = \frac{154}{3} \approx 51.33$ cm $^{2}$
Shaded segment $= 51.33 - 21.2 = 30.13$ cm $^{2}$ (approx.)

Also asked in: 2026 Standard 30/3/2, 2026 Standard 30/3/3

Q384 marksCase StudyAreas Related to Circles CBSE 2026 · Standard 30/1/1

A brooch is crafted from silver wire in the shape of a circle with a diameter of 35 cm. The wire is also used to create 5 diameters, dividing the circle into 10 equal sectors as shown in figure.
Based on the above information, answer the following questions :
(i) What is the radius of circle ? (1)
(ii) What is the circumference of the brooch ? (1)
(iii) (a) What is the total length of silver wire required ? (2)
OR
(iii) (b) What is the area of each sector of the brooch ? (2)

Diagram for CBSE 2026 Class 10 Maths question 38

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Answer: (i) 17.5 cm (ii) 110 cm (iii) (a) 285 cm OR (b) 96.25 cm

^{2}

(i) Radius $= \frac{35}{2} = 17.5$ cm.
(ii) Circumference $= π d = \frac{22}{7} \times 35 = 110$ cm.
(iii) (a) Wire = circumference + 5 diameters $= 110 + 5 \times 35 = 285$ cm.
(iii) (b) Each sector has central angle $3 6^{\circ}$ , i.e. $\frac{1}{10}$ of the circle.
Area $= \frac{1}{10} \times \frac{22}{7} \times 17.5 \times 17.5 = \frac{1}{10} \times 962.5 = 96.25$ cm $^{2}$ .