Question

The area of sector is one-twelfth that of the complete circle. Find the angle of the sector .

Answer 1

We know, $A=\frac{\theta }{360}\times \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{circle}$ .....(i)
Let the area of the circle be Ar.
Thus area of the sector = $\frac{1}{12}Ar$ .....(ii)
From (i) and (ii) we have
$$\begin{gathered} \frac{1}{12}Ar=\frac{\theta }{360}\times Ar \\ \Rightarrow \frac{360}{12}=\theta \\ \Rightarrow \theta =30° \end{gathered}$$