Question

The difference of the areas of a minor sector of angle 120° and its corresponding major sector of a circle of radius 21 cm is ______.

Options

• 231 cm²

• 462 cm²

• 346.5 cm²

• 693 cm²

Answer 1

The difference of the areas of a minor sector of angle 120° and its corresponding major sector of a circle of radius 21 cm is 462 cm².

Explanation:

Given:

radius = 21 cm

Central angle ∠ AOB = 120°

Area of minor sector = `θ/(360°)π "r"^2`

= `(120°)/(360°) xx 22/7 xx 21 xx 21`

= 462 cm²

Area of circle =`π "r"^2`

= `22/7 xx 21 xx 21`

= 1386 cm²

So, Area of major sector = 1386 − 462

= 924 cm²

⇒ Difference of the areas of a minor sector and its corresponding major sector

= 924 - 462

= 462 cm²