Question

the length of the minute hand of a clock is 10 cm then find the distance traveled by it in 21 minutes

Answer 1

$$\begin{gathered} \mathrm{Angle}\mathrm{traced}\mathrm{by}\mathrm{minute}\mathrm{hand}\mathrm{in}1\mathrm{minute}=6° \\ \mathrm{Angle}\mathrm{traced}\mathrm{by}\mathrm{minute}\mathrm{hand}\mathrm{in}21\mathrm{minute}=21\times 6°=126° \\ \mathrm{length}\mathrm{of}\mathrm{minute}\mathrm{hand}=10\mathrm{cm} \\ \mathrm{Now},\mathrm{central}\mathrm{angle}=\mathrm{\theta }=126° \\ \mathrm{radius}\mathrm{of}\mathrm{sector}\mathrm{of}\mathrm{circle},\mathrm{r}=10\mathrm{cm} \\ \mathrm{distance}\mathrm{moved}\mathrm{by}\mathrm{minute}\mathrm{hand}=\mathrm{length}\mathrm{of}\mathrm{arc}=\frac{\mathrm{\theta }}{360°}\times 2\mathrm{\pi r}=\frac{126°}{360°}\times 2\times \frac{22}{7}\times 10=22\mathrm{cm} \end{gathered}$$