# Arc Length Formula

The distance that runs through the curved line of the circle making up the arc is known as the arc length. The arc length is the measure of the distance along the curved line making up the arc. It is longer than the straight line distance between its endpoints. The formula to measure the length of the arc is –

**Arc Length Formula** = \[\LARGE 2\pi r\:\left(\frac{\theta}{360}\right )\]

Where,

r is the radius of the circle.

θ is the central angle of the arc.

### Solved Examples

**Question 1:**Find the arc length if the radius of the arc is 8 cm and its central angle is 40

^{o}?

**Solution:**

Given,

Radius of the arc = r = 8 cm

Central angle of the arc = $\theta$ = 40

= 2$\pi$r $\times$ $\frac{\theta}{360}$

= 2 $\times$ $\pi$ $\times$ 8 $\times$ $\frac{40}{360}$ cm

Radius of the arc = r = 8 cm

Central angle of the arc = $\theta$ = 40

^{o}Arc length,= 2$\pi$r $\times$ $\frac{\theta}{360}$

= 2 $\times$ $\pi$ $\times$ 8 $\times$ $\frac{40}{360}$ cm

= 5.582 cm