SOLUTION: What is the radius of a circle with a sector area of 3 square feet determined by a central angle of 1/4 radian

The area of the whole circle is p·r².

The area A of the sector is to the area of the whole circle as
the central angle of the sector is to 2p, the angle of the
whole circle:

      = 

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

      = 

Cross multiply

     6p = pr²
Divide both sides by p

      6 = r²

Multiply both sides by 4

     24 = r²

    Ö24 = r

   Ö4·6 = r

  Ö4·Ö6 = r

   2·Ö6 = r

Or approximately r = 4.898979486 feet

Edwin