Question 998520
given:  {{{theta=40}}}  and {{{r=20}}}

We can use the arc length {{{L=radius*angle-radians}}}  formula , with {{{theta= 40}}}° and {{{r = 20 }}}



arc-length {{{L=radius*angle-radians}}} 

since {{{(40)}}}°  =  {{{(2pi)/9}}} in radians
we have
{{{L=20*(2pi)/9}}}

{{{L=40pi/9}}}

or, you can do it this way:

whole circumference of a circle is  = {{{2r*pi}}}

if angle = {{{40}}}}° , it is {{{(1/9)}}} of {{{360}}}, then {{{L= (1/9)2r*pi}}}=> then you have
{{{L= (1/9)2*20*pi}}}=>{{{L=40pi/9}}}


2.
given: the measure of the arc is {{{70}}}° and the radius of the circle is {{{r=10}}}

One measure of an arc is the angle formed by the arc at the center of the circle that it is a part of.Remembering that the arc measure is the measure of the central angle,we have


 {{{central-angle=70}}}° 

 {{{L=2pi*10(70/360)}}}

{{{L=20pi*(7/36)}}}

{{{L=cross(20)5pi*(7/cross(36)9)}}}

{{{L=(5pi*7)/9)}}}

{{{L=35pi/9)}}}