Application of Python in Evaluating the Volume of 3D Shapes Using Monte Carlo Simulation

Volume estimation of three-dimensional (3D) objects is fundamental in various scientific and engineering fields. While analytical expressions exist for the simple geometric shapes, they become impractical for complex or irregular structures. Monte Carlo simulation is a statistical method which is based on the random sampling, which offers an efficient numerical alternative. This research explores the application of Monte Carlo integration method for the estimation of the volumes of three different 3D objects viz. sphere, cylinder, and cone. The paper elaborates on the mathematical background of the simulation by presenting detailed Python implementations, and analyzes the accuracy, convergence rates, and computational efficiency of the method. The study concludes that the simulation, despite their probabilistic nature, provide an effective and scalable technique for volume estimation, particularly for the shapes without closed-form volume expressions.