Question

find the length of the arc of the circle of diameter 7cm having area of the sector 3.85cmsq also find the measure of the arc​

Answer 1

Given :-

• Diameter of circle (d) = 7cm
• Area of the sector = 3.85 cm²

To Find :-

• The measure of the arc.

Solution :-

Radius of circle (r) = d/2 = 7/2 = 3.5 cm

Let the angle of centre made by the sector be θ ;

⭐ Area of sector = πr² × θ/360°

[ Putting values ]

↪ 3.85 = 22/7 × (3.5)² × θ/360

↪ θ = 3.85 × 360 × 7/(3.5)² × 22

↪ θ = 9702/12.25 × 22

↪ θ = 9702/269.5

↪ θ = 36°

Let, length of the arc be "L".

We know that,

⭐ Length of the arc = 2πr × θ/360°

[ Putting values ]

↪ L = 2 × 22/7 × 3.5 × 36/360

↪ L = 44 × 0.5 × 0.1

↪ L = 44 × 0.55

↪ L = 2.2 cm

Hence,

• The measure of the arc is 2.2 cm.