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.

In this article, an attempt has been made to explain and model the Taylor table method in Python. A step-by-step algorithm has been developed, and the methodology has been presented for programming. The developed TT_method() function has been tested with the help of four problems, and accurate results have been obtained. The developed function can handle any number of stencils and is capable of producing the results instantaneously. This will eliminate the task of hand calculations and the use can directly focus on the problem solving rather than working hours to descretize the problem.