Volume 2 : 3 ratio of the volumes of the sphere and cylinder is credited to Archimedes. The volume of a sphere is the integral of an infinite number of infinitesimally small circular disks of thickness "dx". The calculation for the volume of a sphere with center 0 and radius "r" is as follows. The surface area of the circular disk is formula_10. The radius of the circular disks, defined such that the x-axis cuts perpendicularly through them, is or where y or z can be taken to represent the radius of a disk at a particular x value. Using y
Phase-contrast X-ray imaging the length of the wave vector, the length of a wave vector with wavelength of 1 Angstrom and the atomic number. The valid formula under these conditions for the phase shift cross section is: where is the atomic number, the length of the wave vector, and the classical electron radius. This results in the following expressions for the two parts of the complex index of refraction: Inserting typical values of human tissue in the formulas given above shows that is generally three orders of magnitude larger than within the diagnostic X-ray range. This implies that the phase-shift of an X-ray