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Several surface measurement methods for determining the volume of deep or layered stone exist. One of the key indicators of coal extraction efficiency in open cast mining is to determine the volume of excavated rock. Procedures for determining the volume have been used for many centuries. Determining the extracted volume or layered material has been a periodically recurring role of mine -surveying practice, and mine surveyors apply different methods for its determination. The incorrect determination of the rock volume may result in large economic losses of the mining enterprise. The choice of the method for determining the volume depends on the deadline by which the determined volume has to be submitted to the superior components or the mining enterprise management, as well as on the requirements for accuracy of the volume determination, and a financial limit beyond which this volume determination has to be done. Secondary conditions for determining the volumes include the level of personnel training in the individual procedures and methods of measuring and calculating volumes, the technical standards of the enterprise, the applied instrumentation, hardware and software. The article compares the values of the accurately defined mathematical solid (a cylindrical segment) to the methods of calculating the volume normally used in mining and surveying practice and programs commonly used to calculate volumes in order to determine the threshold value of the systematic deviation in input measurements to determine the volume. The mathematical model is the basis for determining the correct volumes of the extracted material. The surface of the drawn or layered material does not form a smooth surface as a mathematical model. The process of determining volume errors on the mathematical model has been verified on the real body of coal deposition. The comparison of the determination of the errors between the digital terrain model on the mathematical body and the real homogenization coal stock is presented at the Conclusion of the article.
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