Question

In a circle of radius 6 cm, a chord of length 10 cm makes an angle of 110° at the centre of the circle. Find the area of the sector OAВ.

Answer 1

Given: Circle with radius r = 6 cm, central angle θ = 110°.

Step-wise calculation:

1. Area of a sector = `(θ/360) xx π r^2`.

2. Substitute θ = 110°, r = 6 cm:

`A = (110/360) xx π xx 6^2`

3. Simplify fraction:

`110/360 = 11/36` and 6² = 36 

So `A = (11/36) xx π xx 36` 

= 11π cm²

4. Decimal value:

11π ≈ 34.56 cm²

Area of sector OAB = 11π cm² (≈ 34.56 cm²).