Q. 215.0( 3 Votes )

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 :

Given: Angle of sector = 120°


Radius = 21 cm


To find: Difference of areas


Explanation:



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



= 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.


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