In the same way that definite integrals are computed by adding an infinite number of rectangles to find the total area, the volume of the solid of revolution
related to this region is found by adding the volume of an infinite number of disks created by revolving each rectangle of the region about the axis of rotation.
This can be achieved using the second theorem of Pappus, that states: "The volume V of a solid of revolution
generated by the revolution of a lamina about an external axis is equal to the product of the area A of the lamina and the distance d traveled by the lamina's geometric centroid [bar.x]" .
One exemplary embodiment provides a system comprising: a light source; an image producing unit, which produces an image upon interaction with light approaching the image producing unit from the light source; an eyepiece; and a mirror, directing light from the image to a surface of the eyepiece, wherein the surface has a shape of a solid of revolution
formed by revolving a planar curve at least 180 DEG around an axis of revolution.
Solid of Revolution
constructed in Ti-Nspire Cas and Geogebra 4.2
It is advisable to model the foundation as a solid of revolution
. Its profile could be divided by quadrangle elements MESH200 of desirable density and distribution, specially intended for this type of modeling.