Surfaces of Revolution in "n" Dimensions
IJMEST Volume 38, Number 6, ISSN 0020-739X
This paper provides surface area and volume formulas for surfaces of revolution in R[superscript n]. In addition the authors illustrate how to obtain the formulas for volume and surface areas of revolution about the x- or y-axis in two different ways: a "heuristic" argument and a rigorous calculation using "cylindrical" coordinates. In the last section of this paper, the well known paradoxical phenomenon exhibited by Gabriel's horn is considered.
Aberra, D. & Agrawal, K. (2007). Surfaces of Revolution in "n" Dimensions. International Journal of Mathematical Education in Science and Technology, 38(6), 843-852.