Question

Find the area of sector of a circle with the radius 4cm and the angle ${30}^{\circ }$ also , find the area of the corresponding major sector ( use $\pi$ = 3 . 14 )

Answer 1

Here, $\theta =,{30}^{\circ }$ and $r=4cm$

$\therefore$ Area of sector OPAB $=$ $\frac{\theta }{360}\times \pi r^2=\frac{30}{360}\times 3.14\times 4\times 4c{m}^2$

$=\frac{3.14\times 4}{3}c{m}^2=4.153c{m}^2$

Area of corresponding major sector
= Area of sector OA QB

= $\pi r^2-\frac{\theta }{360}\times \pi r^2$

= $\pi r^2(1-\frac{\theta }{360})$

= $3.14\times 4\times 4(1-\frac{\theta }{360})c{m}^2$

= $3.14\times 4\times 4\times \frac{11}{12}c{m}^2=\frac{3.14\times 44}{3}c{m}^2=46.05c{m}^2$