The radius of the circular disks, defined such that the x-axis cuts perpendicularly through them, is yr2x2displaystyle ysqrt r2-x2 or zr2x2displaystyle zsqrt r2-x2 where y or z can be taken to represent the radius of a disk at a particular x value.Let the solid K (Figure 1) be bounded by a cylindrical surface with generators parallel to the z -axis, by the Jordan-measurable region M of the plane xOy, and by the surface z f(x, y which is intersected by any line parallel to a generator.

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The calculation for the volume of a sphere with center 0 and radius r is as follows.Wolfram Language using, volume reg.

Volume is a function of state and is interdependent with other thermodynamic properties such as pressure and temperature.In their theory of volumes of polyhedrons, Greek mathematicians had to overcome the considerable difficulties that make this branch of geometry substantially different from the related branch dealing with the areas of polygons.E., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces.