Question

In a circle of radius 6.3 cm, an arc AB subtends an angle of 90° at the centre o of the
circle. Find the area of the sector AOB​

Answer 1

Answer:

Radius (r) of circle = 21 cm

Angle subtended by the given arc = 60°

Length of an arc of a sector of angle θ =

Length of arc ACB =

= 22 cm

Area of sector OACB =

In ΔOAB,

∠OAB = ∠OBA (As OA = OB)

∠OAB + ∠AOB + ∠OBA = 180°

2∠OAB + 60° = 180°

∠OAB = 60°

∴ ΔOAB is an equilateral triangle.

Area of ΔOAB =

Area of segment ACB = Area of sector OACB − Area of ΔOAB

Answer 2

Step-by-step explanation:

Area of arc = (angle/360°) × πr^2

A = (90/360) × π × 39.69

= 31.15 cm^2