The diameter of a circle is 120cm, if length of the chord of the arc is 60cm, then the length of an arc of a circle is.........

To find the length of the arc of the circle, we will follow these steps:

Given:
Diameter of the circle = 120 cm
Radius (r) = Diameter / 2 = 120 / 2 = 60 cm
Chord length (c) = 60 cm
Step 1: Find the Central Angle (θ) Subtended by the Chord
Using the chord length formula:

c = 2r sin(θ/2)

Substituting the given values:

60 = 2(60) sin(θ/2)
60 = 120 sin(θ/2)
sin(θ/2) = 60 / 120
sin(θ/2) = 1/2

From trigonometry, we know:

θ/2 = 30°
θ = 60°

Step 2: Find the Length of the Arc
The formula for arc length is:

Arc length (L) = (θ/360) × 2πr

Substituting the values:

L = (60/360) × 2π(60)
L = (1/6) × 120π
L = 20π cm

Approximating π ≈ 3.1416:

L ≈ 20 × 3.1416
L ≈ 62.83 cm

Final Answer:
The length of the arc is 20π cm or approximately 62.83 cm.