Question 979530
If you can find the radius, then
the problem is solved, since
Circumference = {{{ 2*pi*r }}}
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The whole circle is {{{ 360 }}} degrees of arc
{{{ 140 / 360 = 7/18 }}}
Let {{{ A }}} = the area of the whole circle
I can say:
{{{ ( 7/18 )*A = 126*pi }}}
{{{ A = ( 18/7 )*126*pi }}}
{{{ A = 324*pi }}}
I know that:
{{{ A = pi*r^2 }}} ,so
{{{ pi*r^2 = 324*pi }}}
{{{ r^2 = 324 }}}
{{{ r = 18 }}}
and
{{{ C = 2*pi*r }}}
{{{ C = 2*pi*18 }}}
{{{ C = 36*pi }}}
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The perimeter of the shaded rgion is:
{{{ ( 7/18 )*36*pi }}}
{{{ 14*pi }}} answer