Ratio of Surface Area to Volume in Nanotechnology and Nanoscience (Basic Nanomechanics Series)

This is a concise article detailing the derivations of precise and exact equations for the ratio of surface area to volume for certain geometrical shapes. This ratio is very important in nanomaterials as the noticed increase in this ratio provides these types of materials with distinct properties from their bulk counterparts. The ratio of surface area to volume (called SAVR in this work) plays a very important role in nanotechnology and nanoscience. This ratio is calculated here for various simple geometrical shapes including the cube, the sphere, the cylinder, the cone, four types of prisms, four types of pyramids, the tetrahedron, the octahedron, the dodecahedron, and the icosahedron. In addition to calculating SAVR, the article provides also numerical examples of this calculation showing the increase in this ratio for the cube, the sphere, the cylinder, and the cone. This calculation is enhanced with various tables and graphs for SAVR. The article is the first in our new series on basic nanomechanics. The reader is expected to know the basic mathematical concepts and equations taught in beginning courses of algebra and geometry.