Question

find the area of the sector of a circle with radius 4 cm and of Angle 30°.Also find the area of the corresponding major sector.

Answer 1

Step-by-step explanation:

Given:

• Radius of sector is 4 cm.
• Angle of sector is of 30°.

To Find:

• What is the area of the sector and also the area of the corresponding major sector.

Formula to be used:

• Area of sector = θ/360 $\times$ πr²

Solution: Let the given sector be OAPB. (see fig , Taking π = 3.14 )

$\implies{\rm }$ Area of sector (OAPB) = 30/360 x 3.14 x 4 x 4 cm²

$\implies{\rm }$ Area of OAPB = 30/360 x 50.24 cm²

$\implies{\rm }$ Area of OAPB = 1507.2/360 cm²

$\implies{\rm }$ Area of OAPB = 4.19 cm² (approx)

Hence, the area of sector OAPB is 4.19 cm²

∴ Area of corresponding major sector = πr² – area of sector OAPB

$\implies{\rm }$ πr² – 4.19 cm²

$\implies{\rm }$ 3.14 x (4)² – 4.19 cm²

$\implies{\rm }$ 3.14 x 16 – 4.19 cm²

$\implies{\rm }$ 50.24 – 4.19 cm²

$\implies{\rm }$ 46.05 cm² or 46.1 cm² (approx)

Hence, The area of major sector is 46.1 cm²

________________________

★ Alternatively ★

• Area of major sector = (360 – θ)/360 $\times$ πr²

$\implies{\rm }$ (360 – 30/360) $\times$ 3.14 $\times$ 4 $\times$ 4 cm²

$\implies{\rm }$ 330/360 $\times$ 3.14 $\times$ 16 cm²

$\implies{\rm }$ 330/360 $\times$ 50.24 cm²

$\implies{\rm }$ 16579.2/360 cm²

$\implies{\rm }$ 46.05 cm² or 46.1 cm² (approx)