Find the area of the sector of a circle of radius 7 cm and of central angle 90°. Also, find the area of corresponding major sector.

Question :Find the area of the sector of a circle of radius 7 cm and of central angle 90°. Also, find the area of corresponding major sector.

The correct answer :The area of a sector of a circle is given by:

Area of sector = (θ/360) x πr^2

where θ is the central angle in degrees and r is the radius of the circle.

Given, the radius of the circle is 7 cm and the central angle is 90°.

Area of sector = (90/360) x π(7)^2 = (1/4) x 49π = 12.25π ≈ 38.48 cm^2

To find the area of the corresponding major sector, we subtract the area of the minor sector from the area of the whole circle.

The area of the whole circle = πr^2 = π(7)^2 = 49π

Area of major sector = πr^2 – area of minor sector = 49π – 12.25π = 36.75π ≈ 115.27 cm^2

Therefore, the area of the major sector is approximately 115.27 cm^2.