### Theory:

Circumference of the circle:
The circumference of the circle is defined as the pi($$π$$) multiply with the diameter of the circle($$d$$). The degree of the circle is $360\mathrm{°}$.

Circumference of the circle = $$\pi\times d$$ units (where $$d=2\times r$$).

$$= \pi\times 2\times r=2\pi r$$ units

Where $\mathrm{\pi }=3.14$.
Length of the arc of the semicircular quadrant:
The length of the arc of the semicircular quadrant is defined as the one by two($$1/2$$) pi($$π$$) multiply with the diameter of the circle($$d$$). The degree of the semicircle is $$180°$$.

Circumference of the circle = $$\pi\times d$$ units (where $$d=2\times r$$).

$$= \pi\times 2\times r=2\pi r$$ units.

Length of semicircle arc ($$l$$) = $$\frac{1}{2}\times 2\pi r$$ units.

It can also be written as $\frac{180\mathrm{°}}{360\mathrm{°}}×2\mathrm{\pi }r$ units (where the degree of the semicircle is $180\mathrm{°}$).
Length of the arc of the one-third of the circle:
The length of the arc of the one-third of the circle is defined as the one by three($$1/3$$) pi($$π$$) multiply with the diameter of the circle($$d$$). The degree of the one-third of the circle is $$120°$$.

Circumference of the circle = $$\pi\times d$$ units (where $$d=2\times r$$).

$$= \pi\times 2\times r=2\pi r$$ units

Length of the one-third of the circle arc = $$\frac{1}{3}\times 2 \pi r$$ units.

It can also be written as $\frac{120\mathrm{°}}{360\mathrm{°}}×2\mathrm{\pi }r$ units (where the degree of the sector is $120\mathrm{°}$).
Length of the arc of the circular quadrant:
The length of the arc of the circular quadrant is defined as the one by four or quarter($$1/4$$) pi($$π$$) multiply with the diameter of the circle($$d$$). The degree of the arc of the circular quadrant is $$90°$$.

Circumference of the circle = $$\pi\times d$$ units (where $$d=2\times r$$).

$$= \pi\times 2\times r=2\pi r$$ units

Length of the quadrant arc($$l$$) = $$\frac{1}{4}\times 2 \pi r$$ units.

It can also be written as $\frac{90\mathrm{°}}{360\mathrm{°}}×2\mathrm{\pi }r$ units (where the degree of the quadrant is $90\mathrm{°}$).

From the above explanation, we get an idea that the length of the arc is equal to the pi($$π$$) multiply with the diameter of the circle($$d$$) by $\frac{\mathrm{\theta }\mathrm{°}}{360\mathrm{°}}$.

Therefore the length of the arc $l=\frac{\mathrm{\theta }\mathrm{°}}{360\mathrm{°}}×2\mathrm{\pi }r$.
Important!
If a circle of radius($$r$$) units divided into $$n$$ equal sectors, then the length of arc $$=$$ $$\frac{1}{n}\times 2\pi r$$ units.