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