Question

The area of the sector of a circle of radius 10.5 cm is 69.3 cm². Find the central angle of the sector.

Answer 1

Given:
Area of the sector = 63 cm²
Radius = 10.5 cm

Now,
Area of the sector $=\frac{{\mathrm{\pi r}}^2\mathrm{\theta }}{360}$
$$\begin{gathered} \Rightarrow 69.3=\frac{22}{7}\times 10.5\times 10.5\times \frac{\theta }{360} \\ \Rightarrow \theta =\frac{69.3\times 7\times 360}{22\times 10.5\times 10.5} \\ \Rightarrow \theta ={72}^{\circ } \end{gathered}$$

∴ Central angle of the sector = ${72}^{\circ }$