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Mathematics — CBSE Class 10 board question

Q1. [1]
Arc PQ subtends an angle $\theta$ at the centre of the circle with radius 6.3 cm. If $PQ = 11$ cm, then the value of $\theta$ is
  1. A $10^\circ$
  2. B $60^\circ$
  3. C $45^\circ$
  4. D $100^\circ$
Previously asked in CBSE board exam
2026 30/4/1 Q17
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer

Using arc length formula: $l = \dfrac{\theta}{360} \times 2\pi r$

$11 = \dfrac{\theta}{360} \times 2 \times \dfrac{22}{7} \times 6.3$

$11 = \dfrac{\theta}{360} \times 39.6$

$\theta = \dfrac{11 \times 360}{39.6} = 100°$

Answer: (D) 100°

Explanation

The arc length formula from the chapter summary is $l = \dfrac{\theta}{360} \times 2\pi r$. Substitute $l = 11$, $r = 6.3$, $\pi = \frac{22}{7}$, then solve for $\theta$. Note: PQ here refers to the arc length, not the chord. Examiners expect you to state the formula, substitute values, and box the answer clearly.

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