Question

The area of a sector of a circle of radius 14 cm is $77c{m}^2$. Find its central angle.

Answer 1

Given that $r=14cm,area=77c{m}^2$

Area of the sector $=\frac{\theta }{{360}^{\circ }}\times \pi r^2$

$77=\frac{\theta }{{360}^{\circ }}\times \frac{22}{7}\times 14\times 14$

$\therefore \theta =\frac{77\times {360}^{\circ }\times 7}{22\times 14\times 14}={45}^{\circ }$