The large hand of a clock is $42 cm$ long. How much distance does its extremity move in$20$ minutes? 

The large hand of the clock makes a complete revolution in $60$ minutes. 

$\therefore$ Angle traced out by the large hand in$20$ minutes (of time)

$=\frac{{360}^{\circ }\times 20}{60}={120}^{\circ }=\frac{120\pi }{180}\text{ radian }=\frac{2\pi }{3}\text{ radian }$

Hence, the distance moved by the extremity of the 

$\text{ large hand }=\left(42\right)\times \frac{2\pi }{3}=88\mathrm{cm}.(\because l=\mathrm{r}\theta )$