The cylinder x² + y² = x divides the unit sphere S into two regions S₁ and S₂, where S₁ is outside the cylinder and S₂ is inside the cylinder. Find the ratio A(S₁) /A(S₂) of the areas of S₁ and S₂.
a) 2:1
b) 1:2
c) 3:1
d) 1:3