Question

The perimeter of sector OAB of a circle with centre O and radius 5.6 cm, is 15.6 cm. Find length of the arc AB. Also find the value of θ.

Answer 1

Given: r = 5.6 cm, Perimeter = 15.6 cm.

Perimeter = 2r + l

15.6 = 2(5.6) + l

15.6 = 11.2 + l

l = 15.6 – 11.2 = 4.4 cm

Arc length (l) = `θ/360 xx 2πr`

`4.4 = θ/360 xx 2 xx 22/7 xx 5.6`

`4.4 = θ/360 xx 44 xx 0.8`

`4.4 = θ/360 xx 35.2`

`1 = θ/360 xx 8`

8θ = 360

`θ = 360/8`

θ = 45°

The arc length is 4.4 cm and the central angle θ is 45°.