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Many of the natural and industrial objects could be mathematically modeled in rectangular, polar, cylindrical or spherical coordinates depending on their geometrical properties. The examples

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Many of the natural and industrial objects could be mathematically modeled in rectangular, polar, cylindrical or spherical coordinates depending on their geometrical properties. The examples of this mathematical modeling are shown in Figs. 1(a) and (b). Therefore, obtaining the physical components of these objects could be feasible by using multiple integrals. For the apple shown Fig. 1(a) that is featured by rotating the red curve about the zaxis, if we assume that the apple has a uniform density 6 = 2.5 at each point, what is the mass, center of mass and moment of inertia of this apple about the z-axis. For the object shown by blue curves in Fig. 2(b). what is the volume of the object

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