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Mathematics — Standard (041) — CBSE Class 10 board question

Q1. [1] § 11.2 Summary
An arc of length 2.2 cm subtends an angle $\theta$ at the centre of the circle with radius 2.8 cm. The value of $\theta$ is
  1. (A) $50°$
  2. (B) $60°$
  3. (C) $45°$
  4. (D) $30°$
Previously asked in CBSE board exam
2026 30/5/1 Q13
Generated by claude-sonnet-4-6 · 2026-06-15 10:38 · grounding rag
Model Answer

Using the formula: Length of arc $= \dfrac{\theta}{360} \times 2\pi r$

$2.2 = \dfrac{\theta}{360} \times 2 \times \dfrac{22}{7} \times 2.8$

$\theta = \dfrac{2.2 \times 360 \times 7}{2 \times 22 \times 2.8} = \dfrac{5544}{123.2} = 45°$

(C) 45°

Explanation

Use the arc length formula from the chapter summary: $\ell = \frac{\theta}{360} \times 2\pi r$. Substitute $\ell = 2.2$ cm, $r = 2.8$ cm, $\pi = \frac{22}{7}$, and solve for $\theta$. Always use $\pi = \frac{22}{7}$ unless told otherwise.

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