Question

Find the difference of the areas of a sector of angle 120° and its corresponding major sector of a circle of radius 21 cm.

Answer 1

Radius of the circle = r = 21 cm

Area of the circle

Central angle of the sector AOBA = 120°

Central angle of the sector AOBA (in radians) = θ (120π/180) = 2π/3

Now, area of the minor sector AOBA = (1/2)r²θ

= (1/2) × (21)² × (2π/3)

= 462 cm²

Area of the major sector ABOA = Area of the circle – Area of the sector AOBA

= 1386 – 462 = 924 cm²

Now, Difference of the areas of a sector AOBA and its corresponding major sector ABOA

= |Area of major sector ABOA – Area of minor sector AOBA|

= |924-462| = 462 cm²

Hence, the required difference of two sectors is 462 cm².