Question

The length of minute hand of a clock is 5 cm . Find the area swept by the minute hand during the time period 6:05 am and 6:40 am.

Answer 1

Minute hand of the clock describes a circle of radius equal to its length i.e 5 cm.
The minute hand rotates through 6^o in one minute.
So, the minute hand will sweep 210^o in one minute.
Area swept by the minute hand in one minute is the area of a sector of angle 6^o in a circle of radius 5 cm.
Area swept by the minute hand in 35 minutes is the area of a sector of angle 210^o in a circle of radius 5 cm
$\mathrm{Area}\mathrm{of}\mathrm{sector}=\frac{\theta }{360}\times \mathrm{\pi }{r}^2$
$$\begin{gathered} =\frac{210}{360}\times \mathrm{\pi }\times {\left(5\right)}^2 \\ =45\frac{5}{6}{\mathrm{cm}}^2 \end{gathered}$$