And now for the solution of the equations.

Input := 


sol = Solve[{Area3[R2] == 1/3 Pi (2 R)^2, 

				Area1[R1] == 1/3 Pi (2 R)^2},

						{R1, R2}]//N 

Output =


{{R1 -> -0.816497 R, R2 -> -1.1547 R}, 

  {R1 -> -0.816497 R, R2 -> 1.1547 R}, 

  {R1 -> 0.816497 R, R2 -> -1.1547 R}, 

  {R1 -> 0.816497 R, R2 -> 1.1547 R}}