Question

Arc PQ subtends an angle θ at the centre of the circle with radius 6.3 cm. If `hat(PQ)` = 11 cm, then the value of θ is ______.

Options

• 10°

• 60°

• 45°

• 100°

Answer 1

Arc PQ subtends an angle θ at the centre of the circle with radius 6.3 cm. If `hat(PQ)` = 11 cm, then the value of θ is 100°.

Explanation:

Given: l = 11 cm, r = 6.3 cm, `π ≈ 22/7`.

Length of Arc (`l`) = `θ/360^circ xx 2πr`

`11 = θ/360^circ xx 2 xx 22/7 xx 6.3`

`11 = θ/360^circ xx 44 xx 0.9`

`11 = θ/360^circ xx 39.6`

`11/39.6 = θ/360^circ`

`1/3.6 = θ/360^circ`

`θ = 360/3.6`

θ = 100°

The value of θ is 100°.