The minute hand of a clock is 15 cm long and sweeps an area of 15\pi \text{ cm}^2 on the dial of the clock. How much angle does it describe during this period ?
- A. 12^\circ
- B. 18^\circ
- C. 24^\circ ✓
- D. 30^\circ
Correct Answer: C. 24^\circ
Explanation
The area of a sector of a circle is given by Area = \frac{\theta}{360^\circ} \times \pi r^2. Substituting the given values: 15\pi = \frac{\theta}{360^\circ} \times \pi (15)^2. This simplifies to 15 = \frac{\theta}{360^\circ} \times 225, so \theta = \frac{15 \times 360^\circ}{225} = 24^\circ.
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