Question

If length of the circular arc is 10 cm and the radius 3·5 cm, find the area of the sector of the circle.

Answer 1

Length of the circular arc = 10 cm.

Radius = 3.5 cm.

Length of the circular arc = `θ/360^circ xx 2πr`

⇒ 10 = `θ/360^circ xx 2 xx 22/7 xx 3.5`

⇒ θ = `(10 xx 360^circ xx 7)/(2 xx 22 xx 3.5)`

⇒ θ = 163.6°

Now, Area of the sector = `θ/360^circ xx πr^2`

= `163.6/360^circ xx 22/7 xx (3.5)^2`

= 17.5

As a result, the sector's scope is 17.5 sq. cm.