Volumes of intersection for the projection of a 3D radial distribution onto a 2D plane. In grey is the volume of intersection of concentric sphere and cylinder. In blue is the volume of intersection of a spherical shell with radii R_min, R_max with a cylinder of radius ρ_max(in red). The volume of interaction represents the volume contribution from the spherical shell (assumed to have uniform thermodynamical properties) to a circular region of radius ρ (dashed red line). For a cylindrical shell of radii ρ_min and ρ_max (in orange), the area of intersection represents the contribution to the annulus by the shell. Given the azimuthal symmetry of both sphere and cylinder, the polar angle θ is not displayed.