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14. Recall the concept of the circumference and arc length

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

$360 °$ .

Circumference of the circle =

$\pi\times d$ units (where

$d=2\times r$ ).

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

Where

$π = 3.14$ .

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

$\frac{180 °}{360 °} \times 2 π r$ units (where the degree of the semicircle is

$180 °$ ).

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

$\frac{120 °}{360 °} \times 2 π r$ units (where the degree of the sector is

$120 °$ ).

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

$\frac{90 °}{360 °} \times 2 π r$ units (where the degree of the quadrant is

$90 °$ ).

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

$\frac{θ °}{360 °}$ .

Therefore the length of the arc

$l = \frac{θ °}{360 °} \times 2 π r$ .

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.

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14. Recall the concept of the circumference and arc length

Theory: