Find the length of the​ arc, s, on a circle of radius r intercepted by a central angle theta. Express the arc length in terms of π.?

Let's revise fundamentals of circular arcs and it's geometrical properties.

An arc is a segment of a circle around the circumference. An arc measure is an angle

the arc makes at the center of a circle, whereas the arc length is the span along the 

arc. This angle measure can be in radians or degrees, and we can easily convert 

between each with the formula

π radians  = 180°  

We can also measure the circumference, or distance around, a circle. If we take less 

than the full length around a circle, bounded by two radii, we have an arc. That 

curved piece of the circle and the interior space is called a sector, like a slice of 

pizza. When we cut up a circular pizza, the crust gets divided into arcs.

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the arc (s)  length in terms of π

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.....Length of the arc(s)

----------------------------------  =   angle in radians (θ)

 Radius of the circle (r)

....... s

=> -----  =  θ

......  r

=>  s  =  r θ

In the problem Radius ( r )  =  6 "

Angle of Sector (θ)   =  175 degree  =  175 * (π)/180 =  3.054 Radian

 ....................... 6 * 175 * (π)

=>  Hence s = ------------------  =   5.83 (π)   ............ Answer

..........................    180

S = r Θ where the angle is in radians....S = 6 (175 / 180 )π...do the compuations