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Mathematics — CBSE Class 10 board question

Q1. [2]
In the given figure, three sectors of a circle of radius 5 cm, making angles $35^\circ$, $50^\circ$ and $95^\circ$ at the centre are shaded. Find the area of the shaded region. $\left[\text{Use } \pi = \dfrac{22}{7}\right]$
Previously asked in CBSE board exam
2025 30/2/1 Q22 (OR-2)
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer

Total angle of shaded sectors = 35° + 50° + 95° = 180°

Area of shaded region = $\dfrac{\theta}{360} \times \pi r^2$

$$= \frac{180}{360} \times \frac{22}{7} \times 5 \times 5$$

$$= \frac{1}{2} \times \frac{22}{7} \times 25 = \frac{550}{14} = \textbf{39.28 cm}^2$$

Source: Areas Related to Circles, Section 11.1

Explanation

The key insight is that the three sector angles add up to 180°, so the combined shaded region equals a single sector of angle 180° (a semicircle). Apply the formula Area = (θ/360) × πr² directly. Examiners award 1 mark for adding angles correctly and 1 mark for the correct final calculation.

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