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Mathematics — CBSE Class 10 board question

Q1. [1]
The perimeter of the sector of a circle of radius 21 cm which subtends an angle of 60° at the centre of circle, is :
  1. A 22 cm
  2. B 43 cm
  3. C 64 cm
  4. D 462 cm
Previously asked in CBSE board exam
2024 30/5/1 Q8
Generated by claude-sonnet-4-6 · 2026-06-15 10:37 · grounding rag
Model Answer

Perimeter of sector = Arc length + 2r

Arc length = $\dfrac{60}{360} \times 2 \times \dfrac{22}{7} \times 21 = 22$ cm

Perimeter = $22 + 2 \times 21 = 22 + 42 = \mathbf{64}$ cm → Option C

Explanation

Students often confuse "perimeter of sector" with just the arc length. Perimeter includes arc length + two radii. Use the formula: Arc length = $\frac{\theta}{360} \times 2\pi r$, then add $2r$. Here: arc = 22 cm, two radii = 42 cm, total = 64 cm.

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