Quantifying residual oil in a household oil tank

Abstract

On a chilly evening, a practical challenge was posed to 2nd level students taking an extra-curricular math class: Imagine a household cylindrical oil tank lying on its side. How could we determine how much heating oil remains in the tank? In this paper, we ask students to engage in mathematical deduction to devise methods for approximating a solution to this intriguing engineering problem. The only tools that we have access to are measuring tape, and a long clean stick, so resourcefulness becomes key. We establish a mathematical relationship between the parameters that we have access to measure and the volume of oil that remains in the tank. Expanding the scope, we encapsulate this solution within a Jupyter Notebook (Python), allowing for the calculation of oil in any cylindrical tank.