Question

A chord of a circle radius $14\text{cm}$ subtends an angle of ${30}^{\circ }$ at the centre. Find the areas of both, minor sector and major sector of the circle. $(\text{Take}\pi =\frac{22}{7})$.

Answer 1

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

$=\frac{30}{360}\times \frac{22}{7}\times 14\times 14{\text{cm}}^2$

$=\frac{154}{3}{\text{cm}}^2$

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

$=[(\frac{22}{7}\times 14\times 14)-(\frac{30}{360}\times \frac{22}{7}\times 14\times 14)]{\text{cm}}^2$

$=(616-\frac{154}{3}){\text{cm}}^2$

$=564.6{\text{cm}}^2$