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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 $360\mathrm{\xb0}$.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 $\frac{180\mathrm{\xb0}}{360\mathrm{\xb0}}\times 2\mathrm{\pi}r$ units (where the degree of the semicircle is $180\mathrm{\xb0}$).

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 $\frac{120\mathrm{\xb0}}{360\mathrm{\xb0}}\times 2\mathrm{\pi}r$ units (where the degree of the sector is $120\mathrm{\xb0}$).

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 $\frac{90\mathrm{\xb0}}{360\mathrm{\xb0}}\times 2\mathrm{\pi}r$ units (where the degree of the quadrant is $90\mathrm{\xb0}$).

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 $\frac{\mathrm{\theta}\mathrm{\xb0}}{360\mathrm{\xb0}}$.**Therefore the length of the arc**$l=\frac{\mathrm{\theta}\mathrm{\xb0}}{360\mathrm{\xb0}}\times 2\mathrm{\pi}r$.

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.