Question 278218
Find the area to the nearest hundredth of a 10 degree sector
in a circle with diameter of 12 centimeters
<pre><font size = 4 color = "indigo"><b>
That's the red thing below that looks like a thin piece of pie:

{{{drawing(400,400,-7,7,-7,7,

arc(0,0,12,-12,5,355), red(arc(0,0,12,-12,355,360)), 

red(arc(0,0,12,-12,0,5)), red(line(0,0,6*cos(5*pi/180),6*sin(5*pi/180))),
red(line(0,0,6*cos(5*pi/180),-6*sin(5*pi/180))), locate(3,.9,"r=12"),
locate(3,.25,"10°") 


)}}}

The formula is {{{A=(1/2)theta*r^2}}} if {{{ theta }}} is in radians.

So we first change {{{ theta }}} from degrees to radians:

{{{theta="10°"=("10°")(pi/"180°")=pi/18}}}

{{{A=(1/2)theta*r^2}}}

becomes

{{{A=(1/2)(pi/18)*12^2= 12.56637061}}} square units.

Edwin</pre>