Question:
The minute hand of a clock is 7.5 cm long. Find the area of the face of the clock described by the minute hand in 56 minutes.
Solution:
The length of minute hand of clock $=7.5 \mathrm{~cm}$.
The angle made by minute hand in 60 minutes $=360^{\circ}$.
The angle made by minute hand in 1 minute $=6^{\circ}$.
The angle made by minute hand in 56 minutes $=56 \times 6^{\circ}=336^{\circ}$.
So, the area of clock described by minute hand in 56 minutes = area of sector with angle $336^{\circ}=\pi r^{2} \times \frac{\theta}{360^{\circ}}=\frac{22}{7} \times 7.5 \times 7.5 \times \frac{336^{\circ}}{360^{\circ}}=165 \mathrm{~cm}^{2}$.