OAB is sector of a circle with centre O and radius 7 cm. If length of arc AB = 22/3 cm, then ∠AOB is equal to (A) (120/7 )° (B) 45° (C) 60° (D) 30°

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/6/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2025: question 10

Set in the CBSE Class 10 board exam of 2025, paper 430/6/1, section A, question 10, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q10 · 1 mark · MCQAreas Related to Circles

OAB is sector of a circle with centre O and radius 7 cm. If length of arc $A B = \frac{22}{3}$ cm, then $∠$ AOB is equal to

(A) $(\frac{120}{7})^{\circ}$
(B) $4 5^{\circ}$
(C) $6 0^{\circ}$
(D) $3 0^{\circ}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/6/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Recall the formula for the length of an arc.

Hint 2

Substitute $r = 7$ and solve for $θ$ .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Arc length $= \frac{θ}{36 0 ^{\circ}} \times 2 π r$ , so $\frac{θ}{360} \times 2 \times \frac{22}{7} \times 7 = \frac{22}{3}$ .
This simplifies to $\frac{44 θ}{360} = \frac{22}{3}$ , giving $θ = 6 0^{\circ}$ .
1 mark

Answer: 60°, option (C)

Where the marks are

Applies the arc length formula to get 60° (1 mark)

Revise the chapter

Chapter: Areas Related to Circles (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Areas Related to Circles, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 430/6/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 10

Hints

Step-by-step solution

Revise the chapter

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