An arc of a circle of radius 10 cm subtends a right angle at the centre of the circle. Find the area of the corresponding major sector. (Use $\pi = 3 \cdot 14$)
Generated by claude-sonnet-4-6 · 2026-06-15 10:37 · grounding rag
Model Answer
Given: radius $r = 10$ cm, angle of minor sector $\theta = 90°$, $\pi = 3.14$
Angle of major sector $= 360° - 90° = 270°$
Area of major sector $= \dfrac{\theta}{360} \times \pi r^2$
$$= \frac{270}{360} \times 3.14 \times 10 \times 10$$
$$= \frac{3}{4} \times 314$$
$$= 235.5 \text{ cm}^2$$
The area of the corresponding major sector is 235.5 cm².
Source: Areas of Sector and Segment of a Circle, Chapter 11
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Explanation
- The arc subtends 90° at the centre, so that is the minor sector angle. The major sector angle = 360° − 90° = 270°.
- Use the formula: Area of sector $= \dfrac{\theta}{360} \times \pi r^2$ directly with $\theta = 270°$.
- Alternatively, find the area of the minor sector first and subtract from $\pi r^2$; both methods give 235.5 cm².
- Remember to use $\pi = 3.14$ as instructed, not $\dfrac{22}{7}$.