Nuclear science and engineering is a field increasingly dominated by computational studies resulting from increasingly powerful computational tools. As a result, analytical studies, which previously pioneered nuclear engineering, are increasingly viewed as secondary or unnecessary. However, analytical solutions to reduced-fidelity models can provide important information concerning the underlying physics of a problem and aid in guiding computational studies. Similarly, there is increased interest in sensitivity analysis studies. These studies commonly use computational tools. However, providing a complementary sensitivity study of relevant analytical models can lead to a deeper analysis of a problem. This work provides the analytical sensitivity analysis of the one-dimensional (1D) cylindrical mono-energetic neutron diffusion equation using the forward sensitivity analysis procedure (FSAP) developed by Cacuci. Further, these results are applied to a reduced-fidelity model of a spent nuclear fuel cask, demonstrating how computational analysis might be improved with a complementary analytic sensitivity analysis.