Question

Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.

Answer 1

Given,

Radius = 5 cm

Length of arc = 3.5 cm

Let θ = angle subtended at the centre of circle

We know that,

Length of arc = θ/360 ∗ 2πr cm

= θ/360 ∗ 2π(5)

From the question, we can equate

3.5 = θ/360 ∗ 2π(5)

3.5 = 10π ∗ θ/360

θ = 360 x 3.5/ (10π)

θ = 126/ π

Now, the area of the sector = θ/360 ∗ πr²

= (126/ π)/ 360 ∗ π(5)²

= 126 x 25 / 360 = 8.75

Hence, the area of the sector = 8.75 cm²