Calculations of liquid/vapor/metal volumes and surface areas The following references help describe the calculations -V_liquid: http://www.mathalino.com/reviewer/derivation-formulas/derivation-formula-volume-sphere-integration -A_surfaceVL: http://tutorial.math.lamar.edu/Classes/CalcI/MoreVolume.aspx -A_surfaceWL: https://en.wikipedia.org/wiki/Spherical_cap