Find the difference of areas of a sector of angle `120^(@)` and its corresponding major sector of a circle of radius 21cm.

Explanation

Given that, radius of the circle ( r) = 21 cm and central angle of the sector `AOBA(theta)= 120^(@)`
So, area of the circle = `pir^(2) = (22)/(7)xx(21)^(2) = (22)/(7)xx21xx21`
= `22xx3xx21 = 1386cm^(2)`
Now , erea of the minor sector AOBA with central angle `120^(@)`
= `(pir^(2))/(360^(@))xxtheta = (22)/(7)xx(21xx21)/(360^(@))xx120`
= `(22xx3xx21)/(3) = 22 xx 21 = 462cm^(2)`
`:.` Area of the major sector ABOA
= Area of the circle - Area of the sector AOBA
= `1386 - 462 = 924 cm^(2)`
`:.` Difference of the areas of a sector AOBA and its corresponding major secjor sector ABOA
= |Area of major sector ABOA - Area of minor sector AOBA|
= `|924 - 462| = 462 cm^(2)`
Hence, the required difference of two sectors is `462 cm^(2)` .