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.

Answer 1

The length of minute hand of clock = 7.5 cm.
The angle made by minute hand in 60 minutes = $360°.$
The angle made by minute hand in 1 minute = $6°.$
The angle made by minute hand in 56 minutes = $56\times 6°=336°.$
So, the area of clock described by minute hand in 56 minutes = area of sector with angle $336°=\mathrm{\pi }{r}^2\times \frac{\theta }{360°}=\frac{22}{7}\times 7.5\times 7.5\times \frac{336°}{360°}=165{\mathrm{cm}}^2.$