Question 1087309
Is the length of the sector 32 ft?
If this is so:
The length of the whole circumference would be
{{{ 2*pi*r }}} where {{{ r }}} is in feet
The entire circle has an angle of {{{ 2*pi }}} radians
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I can write a proportion:
{{{ ( 3*pi/5 ) / ( 2*pi ) = 32/( 2*pi*r) }}}
{{{ ( 3/5 ) / 2 = 16 / ( pi*r ) }}}
{{{ 3/10 = 16 / ( pi*r ) }}}
{{{ 3*pi*r = 160 }}}
{{{ r = ( 160/3 )/pi }}}
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If {{{ A }}} is the area of the sector,
Here is another proportion:
{{{ A / ( pi*r^2 ) = ( (3*pi)/5 ) / ( 2*pi ) }}}
{{{ A / ( pi*r^2 ) = 3/10 }}}
{{{ A = (3/10)*pi*r^2 }}}
{{{ A = (3/10)*pi*(160/3)^2/pi^2 }}}
{{{ A = (3/10)*pi*( 25600/9 )/pi^2 }}}
{{{ A = 2560/( 3*pi) }}}
{{{ A = 853.333/pi }}}
{{{ A = 271.624 }}} ft2
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I could easily have made a mistake
Check the math & get another opinion!