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For the purpose of learning multidimensional models, difficult for perception, representations and technology (device) of the description and measurement of volume and amount of the substance filling the volume of multidimensional objects are considered. Alternative options of multidimensional set of one-dimensional models and unified multidimensional model of three-dimensional objects are compared. The technology of measurement of multidimensional volume and amount of the substance that fills volume is shown. The authors came to the conclusion when transferring from a set of coordinate vectors of material points in complete spatial angle 4π steradian to multidimensional model of in pairs orthogonal vectors, calculation of volume of a multidimensional object significantly becomes simpler. The conclusion is that potentially infinite-dimensional model of an object represents the sphere in which balk of volume, the quantity and energy of the substance filling volume are entirely concentrated on its surface.