Prismoid Sentence Examples
If R and S are the ends of a prismoid, A and B their areas, h the perpendicular distance between them, and C the area of a section by a plane parallel to R and S and midway between them, the volume of the prismoid is *h(A+4C+B).
The most instructive is to regard the prismoid as built up (by addition or subtraction) of simpler figures, which are particular cases of it.
Then the prismoid is divided into a pyramid with vertex P and base ABCD ..., and a series of tetrahedra, such as PABa or PAab.
By (i) and (iii), the formula holds for each of these figures; and therefore it holds for the prismoid as a whole.
In the ordinary case three of the four lateral surfaces of the prismoid are at right angles to the two ends.Advertisement
This formula applies to such figures as the cone, the sphere, the ellipsoid and the prismoid.
The proposition can then be established for a prismoid generally by the method of § 27 (iv).