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Mathematics — CBSE Class 10 board question

Q1. [1]
A piece of wire 20 cm long is bent into the form of an arc of a circle of radius $\dfrac{60}{\pi}$ cm. The angle subtended by the arc at the centre of the circle is:
  1. A $30°$
  2. B $60°$
  3. C $90°$
  4. D $50°$
Previously asked in CBSE board exam
2025 30/1/1 Q18
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer

Arc length = $\dfrac{\theta}{360} \times 2\pi r$ ⟹ $20 = \dfrac{\theta}{360} \times 2\pi \times \dfrac{60}{\pi}$ ⟹ $20 = \dfrac{\theta}{360} \times 120$ ⟹ $\theta = 60°$. Answer: (B) 60°

Explanation

Use the arc length formula from the summary: $l = \dfrac{\theta}{360} \times 2\pi r$. Substitute $l = 20$ cm and $r = \dfrac{60}{\pi}$ cm — the $\pi$ cancels neatly, giving $\theta = 60°$. The key trick is noticing the radius is given as $\dfrac{60}{\pi}$ precisely so $\pi$ cancels.

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