May 25, 2024

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Arc Length Formula

The Length of an Arc of a Circle National 5 - YouTube

The arc length formula is used to infer the length that is made up by the arc. The formula to get the extent of the arc is:

The extent of the arc = 2πr (  Θ  / 360)

In this above-illustrated formula for the extent of the Arc, 

Θ= Central angle,

r = Radius of a given Arc.

Arc

The arc can be interpreted as the length of the curve that unites the two verge junctures. The arc can also be analysed as a part of a circle that is the girth of the circle. Arc is a portion of any provided curve. 

Central Angle

The central angle can be interpreted as an angle or a portion, established by the result of the junction of the two radii of the provided circle.  

Examples of Arc Length Formula

The Examples are one of the best ways to clear the learned topics and also a way to solve further problems of the learned concept.

Example 1: There is an angle given in which the arc is of π/99. The radius provided for this is 67 units. One has to get the extent of the arc. 

Solution:

                 We have been provided with a few data such as,  

       Θ= π/99

                  and,

                  r = 67 units 

                  Now, the formula to get the extent of the arc is already illustrated above and that is, 

                  2πr (Θ /  360),

                  Here, we can also write 

                360= 2π, for an easy calculation

                  Now, implementation of all the provided values in the illustrated formula should be done. 

                  We will get,

                  2π * 67 * ( π /99  / 2π )

                  Now, the 2π will get cancelled, since we already have done that for easy calculation.

                  The remaining value will be,

                   67* π / 99.

                   One can solve this and get the value as an extent of the arc.

Example 2: There is an angle given in which the arc is of 2π/990. In this, the extent of the radius is 450 units. One has to get the extent of the arc.

Solution:

      We have been provided with a few data such as, 

                  Θ= 2π / 990

                  and,

                  r = 450 units

                  Now, to get the extent of the arc, the formula has already been mentioned above, 

                  2πr (Θ/ 360 ),

                  Here, we can also write 360 = 2π, for an easy calculation.

                  Now, by putting all the provided values in the illustrated formula, we will  get,

                   2π * 450 * ( 2π/990  / 2π ),

                   Now,

                   2π will get cancelled and we will be left with,

                   450* (2π / 990 )

                   This will be the extent of the arc.

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