The minute hand of a clock is 14 cm long. Find the area on the face of the clock described by the minute hand in 5 minutes.
Generated by claude-sonnet-4-6 · 2026-06-15 10:37 · grounding rag
Model Answer
In 5 minutes, the minute hand rotates through an angle:
$$\theta = \frac{5}{60} \times 360° = 30°$$
Area swept = Area of sector $= \dfrac{\theta}{360} \times \pi r^2$
$$= \frac{30}{360} \times \frac{22}{7} \times 14 \times 14$$
$$= \frac{1}{12} \times \frac{22}{7} \times 196 = \frac{1}{12} \times 616 = \frac{154}{3} \approx 51.33 \text{ cm}^2$$
Area swept by the minute hand in 5 minutes = $\dfrac{154}{3}$ cm²
Source: Areas of Sector and Segment of a Circle, Chapter 11
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Explanation
- The key step is converting 5 minutes into degrees: the minute hand completes 360° in 60 minutes, so 5 minutes = 30°.
- Then apply the sector area formula directly with r = 14 cm and θ = 30°.
- Examiners expect the angle conversion to be shown explicitly — don't skip it.
- Leave the answer as $\frac{154}{3}$ cm² or write ≈ 51.33 cm²; both are acceptable.