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 length of the arc AB.

Answer 1

Given:

Radius r = 6 cm

Central angle ∠AOB = 110°

Step-wise calculation:

1. Formula: length of an arc s = r·θ, where θ is in radians.

2. Convert angle to radians:

`110^circ = (110 · π)/180` 

= `(11π)/18` radians

3. Apply the formula:

s = r·θ 

= `6 · ((11π)/18)` 

= `((66π)/18)`

= `(11π)/3` cm

4. Decimal value (for convenience):

`(11π)/3 ≈ 11.5192… ≈ 11.52` cm

Length of arc AB = `(11π)/3` cm ≈ 11.52 cm.