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Mathematics — CBSE Class 10 board question

Q1. [1]
A circle is divided into 16 identical sectors. If radius of the circle is 7 cm, area of each sector is
  1. A $\dfrac{77}{4}$ cm²
  2. B $77$ cm²
  3. C $154$ cm²
  4. D $\dfrac{77}{8}$ cm²
Previously asked in CBSE board exam
2026 30/4/1 Q9
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer

Each sector's angle = 360°/16 = 22.5°. Area of each sector = $\dfrac{22.5}{360} \times \dfrac{22}{7} \times 7 \times 7 = \dfrac{1}{16} \times 154 = \dfrac{77}{8}$ cm². Answer: (D)

Explanation

Since 16 identical sectors make a full circle, each sector is simply 1/16 of the total circle area. Total area = πr² = (22/7) × 49 = 154 cm². Dividing by 16 gives 77/8 cm². Watch out for option A (77/4, which would be for 8 sectors) — a common trap.

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