Find the area of the sector of a circle with radius 4 cm and θ=30∘. Also, find the area of the corresponding major sector. (Use π=3.14)

Given that

r = 4 cm

and

θ = 30^{\circ}

To find the area of the sector and the area of the corresponding major sector, use the following formula;
Area of a sector making an angle

θ

at the centre is

π r^{2} (\frac{θ}{360^{\circ}})

.
Area of the corresponding major sector is given by

π r^{2} (1 - \frac{θ}{360^{\circ}})

.
Now substitute

r = 4 cm

and

θ = 30^{\circ}

into

π r^{2} (\frac{θ}{360^{\circ}})

and find the area of the sector. Therefore, the area of the sector

= π \times 4^{2} (\frac{30}{360})

\Rightarrow Area of the sector = \frac{1}{12} \times 3.14 \times 16

\Rightarrow Area of the sector = 4.19 {cm}^{2}

Substitute

r = 4 cm

and

θ = 30^{\circ}

into

π r^{2} (1 - \frac{θ}{360^{\circ}})

and find the area of the corresponding major sector.
Therefore, the area of the corresponding major sector

= \frac{11}{12} \times 3.14 \times 16

\Rightarrow Area of the corresponding major sector = 46.1 {cm}^{2}

Hence, the area of sector and corresponding major sector are

4.19 {cm}^{2}

and

46.1 {cm}^{2}

respectively.
Therefore, option 1 is correct.

Find the area of the sector of a circle with radius $4 cm$ and $θ = 30^{\circ}$ . Also, find the area of the corresponding major sector.

(Use $π = 3.14$ )