Question 641846
What is the radius of a circle with a sector area of 3 square feet determined by a central angle of 1/4 radian
<pre>
{{{drawing(400,400,-1.2,1.2,-1.2,1.2, 

red(arc(0,0,2,-2,-8,8),line(cos(8*pi/180),sin(8*pi/180),0,0), line(cos(8*pi/180),-sin(8*pi/180),0,0)),green(arc(0,0,2,-2,8,352)) )}}}

The area of the whole circle is <font face = "symbol">p</font>·r².

The area A of the sector is to the area of the whole circle as
the central angle of the sector is to 2<font face = "symbol">p</font>, the angle of the
whole circle:

     {{{A/(pi*r^2)}}} = {{{(1/4)/(2pi)}}}

We are told that the area A of the sector  is 3 sq. ft.

     {{{3/(pi*r^2)}}} = {{{(1/4)/(2pi)}}}

Cross multiply

     6<font face = "symbol">p</font> = {{{1/4}}}<font face = "symbol">p</font>r²
Divide both sides by <font face = "symbol">p</font>

      6 = {{{1/4}}}r²

Multiply both sides by 4

     24 = r²

    <font face="symbol">Ö</font><span style="text-decoration: overline">24</span> = r

   <font face="symbol">Ö</font><span style="text-decoration: overline">4·6</span> = r

  <font face="symbol">Ö</font><span style="text-decoration: overline">4</span>·<font face="symbol">Ö</font><span style="text-decoration: overline">6</span> = r

   2·<font face="symbol">Ö</font><span style="text-decoration: overline">6</span> = r

Or approximately r = 4.898979486 feet

Edwin</pre>