Question

The area of a circle is 25π sq.cm. Find the length of its arc subtending an angle of 144° at the centre. Also find the area of the corresponding sector.

Answer 1

Let r be the radius of the circle.

Then πr² = 25π

∴ r² = 25

∴ r = 5 cm

Also, θ = 144° 

= `(144 × π/180)^"c"`

= `(4π^"c")/5`

∴ length of the arc = S = rθ

= `5 × (4π)/5`

= 4π cm

Area of the corresponding sector = `1/2r^2θ`

= `1/2 × (5)^2 × ((4π)/5)`

= 10π sq cm.