Question 1116761
The circumference, {{{ C }}} is:
{{{ C = 2*pi*r }}}
{{{ r = 12 }}} mm
{{{ C = 2*pi*12 }}}
{{{ C = 24pi }}}
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There are {{{ 2pi }}} radians of arc in a circle
{{{ (( 7pi )/6 ) / ( 2pi ) = a / ( 24pi ) }}}
Multiply both sides by {{{ 2pi }}}
{{{ ( 7pi )/6 = a/12 }}}
Multiply both sides by {{{ 6 }}}
{{{ 7pi = a/2 }}}
{{{ a = 14pi }}}
The length of the arc is 14pi mm
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This seems about right. One-half of the circumference
would be {{{ 24pi/2 = 12pi }}}
And {{{ 7pi/6 }}} is a little more than half of {{{ C }}}
so, {{{ 14pi }}} seems gight