Question

Find the area of the sectpr of circle with radius 4 cm and angle 30 degree also find area if corresponding major sector

Answer 1

area of sector =30/360×πr²

1/3×22/7×4×4

22×4/3×7=88/21

therefore the area of minor sector =88/21

area of major sector=area of circle-area of minor sector

==πr²-88/21

=(22/7×4×4)-(88/21)

=(22×16/7)-(88/21)

=352/7-88/21

=1056-88/21

=968/21 or 46.09

Answer 2

Here,

r = 4cm

$\sf{\theta=30°}$

Area of the sector OAPBO

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

= $\sf{ \frac{30}{360} \times 3.14 \times 4 \times 4 {cm}^{2}}$

= $\sf{ \frac{12.56}{3} {cm}^{2}}$

= $\sf{ {4.19cm}^{2} (approx.)}$

Area of the corresponding major sector OAQBO

= Area of the circle - Area of the sector OAPBO

= $\sf{3.14×4×4-4.19){cm}^{2}}$

= $\sf{(50.24-4.19){cm}^{2}}$

= $\sf{{46.05cm}^{2}}$

= $\sf{{46.1cm}^{2}(approx.)}$