The minute hand of a clock is 21 cm long. What is the area on the face of the clock described by the minute hand between 10-10 a.m and 10-30 a.m? (take \pi=\frac{22}{7})
- A. 231\text{ cm}^{2}
- B. 331\text{ cm}^{2}
- C. 462\text{ cm}^{2} ✓
- D. 492\text{ cm}^{2}
Correct Answer: C. 462\text{ cm}^{2}
Explanation
Time passed is 20 minutes. The minute hand covers 360^{\circ} in 60 minutes, so in 20 minutes it covers 120^{\circ}. Area of the sector = \frac{\theta}{360} \pi r^2 = \frac{120}{360} \times \frac{22}{7} \times (21)^2 = \frac{1}{3} \times \frac{22}{7} \times 441 = 462\text{ cm}^2.
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