Question

Solve this:
Q.20. Find the radius of a circle in which an arc of central angle 60$°$ has length of 2$\pi$ cm. Hence find the area of the sector formed by this arc.
[Ans. Area of sector formed by arc = $18\frac{6}{7}c{m}^2$]

Answer 1

Dear Student,

$$\begin{gathered} centralangle=60° \\ perimeterofcircle=2\mathrm{\pi r} \\ \mathrm{length}\mathrm{of}\mathrm{arc}\mathrm{with}\mathrm{central}\mathrm{angle}60°=\frac{60}{360}\times 2\mathrm{\pi r} \\ \Rightarrow \frac{\mathrm{\pi r}}{3} \\ \mathrm{it}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{length}\mathrm{of}\mathrm{arc}\mathrm{is}2\mathrm{\pi } \\ \mathrm{Hence}\frac{\mathrm{\pi r}}{3}=2\mathrm{\pi } \\ \Rightarrow \mathrm{r}=6 \\ \mathrm{Area}\mathrm{of}\mathrm{sector}\mathrm{formed}\mathrm{by}\mathrm{arc}=\frac{60}{360}\times \mathrm{\pi }\times {\mathrm{r}}^2 \\ \Rightarrow \frac{1}{6}\times \frac{22}{7}\times 6\times 6 \\ \Rightarrow \frac{22\times 6}{7} \\ \Rightarrow \frac{132}{7} \\ \Rightarrow 18\frac{6}{7} \end{gathered}$$

Regards,