You are working as a summer intern at a company and a fellow intern (obviously an U of A engineering student) accidently opened the wrong valve and dumped some unknown volume of oil ( gamma 0 = 0.918) into a vat of sea water ( gamma sw = 1.028) forming a stratified (layered) fluid column. The vat is known to have a diameter of 3 m. The engineers at the firm need to know the volume of the oil that had been dumped into the vat and you are tasked with giving them a value. Earlier in the summer you had been playing with a 20 cm diameter, 15 cm tall piece of wood which you found floats with 3.75 cm above the surface in pure water. a) Develop an equation for the volume of the oil as a function of the height from the surface of the oil to the top of the wooden cylinder when it is placed in this stratified fluid column and b) the volume of the oil when the height above the oil surface is 3.5 cm.