# Formula for Length of Arc of Circle with Examples

Here you will learn what is the formula for length of arc of circle with examples based on it.

Let’s begin –

## What is an Arc ?

Arc is a piece of circle. In the figure AB is an arc.

The area OAB in the figure is called sector of the circle.

## Formula for Length of Arc of Circle

Let an arc AB make an angle $$\theta$$ < 180 at the centre of circle of radius r.

Then,

Length of the arc = $$2\pi r \theta\over 360$$

i.e. $$l$$ =  $$\pi r \theta\over 180$$

Also Read : Area of a Ring – Formula and Examples

Example : A sector is cut from a circle of radius 42 cm. The angle of the sector is 120. Find the length of its arc.

Solution : Here r = 42 cm and $$\theta$$ = 120

Length of arc of sector of angle $$\theta$$ and radius r = $$l$$ = $$\pi r \theta\over 180$$

$$\implies$$   $$l$$ = $$120\over 180$$ $$\times$$ $$22\over 7$$ $$\times$$ 42 = 88 cm

Hence, length of arc is 88 cm.

Example : A pendulum swings through an angle 60 and describes an arc 8.8 cm in length. Find the length of the pendulum.

Solution : Here, length of arc ($$l$$) = 8.8 cm and $$\theta$$ = 60

Length of arc of sector of angle $$\theta$$ and radius r = $$l$$ = $$\pi r \theta\over 180$$

$$\implies$$   8.8 = $$60\over 180$$ $$\times$$ $$22\over 7$$ $$\times$$ r

$$\implies$$  r = $$8.8 \times 180 \times 7\over 60 \times 22$$

$$\implies$$ r = $$4.4 \times 3 \times 7\over 11$$  cm = 8.4 cm

Hence, length of pendulum is 88 cm.