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

Given that, radius of the circle (r) = 21 cm and central angle of the sector AOBA (θ) = 120°

So, area of the circle

= πr²

= `22/7 xx (21)^2`

= `22/7 xx 21 xx 21`

= 22 × 3 × 21

= 1386 cm²

Now, area of the minor AOBA with central angle 120°

= `(pi"r"^2)/360^circ xx θ`

= `22/7 xx (21 xx 21)/360^circ xx 120`

= `(22 xx 3 xx 21)/3`

= 22 × 21

= 462 cm²

∴ Area of the major sector ABOA

= Area of the circle – Area of the sector AOBA

= 1386 – 462

= 924 cm²

∴ 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.