Surface Area
Surface area is the Area of a given surface. Roughly speaking, it is the ``amount'' of a surface,and has units of distance squares. It is commonly denoted 
for a surface in 3-D, or 
for a region ofthe plane (in which case it is simply called ``the'' Area).
If the surface is Parameterized using 
and 
, then
 | (1) |
and 
are tangent vectors and 
is the Cross Product.The surface area given by rotating the curve 
from 
to 
about the 
-axis is
 | (2) |
is defined over a region 
, then | (3) |
The following tables gives surface areas for some common Surfaces. In the first table, denotes thelateral surface, and in the second, 
denotes the total surface. In both tables, 
denotes the Radius, 
theheight, 
the base Perimeter, and 
the Slant Height (Beyer 1987).
| Surface | |
| Cone |  |
| Conical Frustum |  |
| Cube |  |
| Cylinder |  |
| Lune (Solid) |  |
| Oblate Spheroid |  |
| Prolate Spheroid |  |
| Pyramid |  |
| Pyramidal Frustum | |
| Sphere |  |
| Torus |  |
| Zone | |
| Surface | |
| Cone |  |
| Conical Frustum |  |
| Cylinder |  |
Even simple surfaces can display surprisingly counterintuitive properties. For instance, the surface of revolution of 
around the x-Axis for 
is called Gabriel's Horn, and has Finite Volume butInfinite surface Area.
References
Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 127-132, 1987.
- Dixon's Theorem
- D-Number
- Dobinski's Formula
- Dodecadodecahedron
- Dodecagon
- Dodecagram
- Dodecahedral Conjecture
- Dodecahedral Graph
- Dodecahedral Space
- Dodecahedron
- Dodecahedron 2-Compound
- Dodecahedron-Icosahedron Compound
- Dodecahedron Stellations
- Domain
- Domain Invariance Theorem
- Dome
- Dominance
- Domino
- Domino Problem
- Donaldson Invariants
- Donkin's Theorem
- Donut
- Doob's Theorem
- Dot
- Dot Product