Platonic solid the inradius "r". That is, The following table lists the various radii of the Platonic solids together with their surface area and volume. The overall size is fixed by taking the edge length, "a", to be equal to 2. The constants "φ" and "ξ" in the above are given by Among the Platonic solids, either the dodecahedron or the icosahedron may be seen as the best approximation to the sphere. The icosahedron has the largest number of faces and the largest dihedral angle, it hugs its inscribed sphere the most tightly, and its surface area to volume ratio is closest
Volume as volume divided by mass. Specific volume is a concept important in thermodynamics where the volume of a working fluid is often an important parameter of a system being studied. The volumetric flow rate in fluid dynamics is the volume of fluid which passes through a given surface per unit time (for example cubic meters per second [m s]). In calculus, a branch of mathematics, the volume of a region "D" in R is given by a triple integral of the constant function formula_1 and is usually written as: The volume integral in cylindrical coordinates is and the volume integral