Surface area
Surface area
The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat polygonal faces), for which the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration.
Common formulas
| Shape | Equation | Variables |
|---|---|---|
| Cube | s = side length | |
| Cuboid | ℓ = length, w = width, h = height | |
| Triangular prism | b = base length of triangle, h = height of triangle, l = distance between triangular bases, a, b, c = sides of triangle | |
| All prisms | B = the area of one base, P = the perimeter of one base, h = height | |
| Sphere | r = radius of sphere, d = diameter | |
| Spherical lune | r = radius of sphere, θ = dihedral angle | |
| Torus | r = minor radius (radius of the tube), R = major radius (distance from center of tube to center of torus) | |
| Closed cylinder | r = radius of the circular base, h = height of the cylinder | |
| Lateral surface area of a cone | ................ | ............ |
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