Surface area

Surface area is the measure of how much exposed area a solid object has, expressed in square units. Mathematical description of the surface area is considerably more involved than the definition of arc length of a curve.

For polyhedra (objects with flat polygonal faces) 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 the surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration.

 Common formulas

Surface areas of common solids
Shape Variables
Cube s = side length
Rectangular prism = length, w = width, h = height
Sphere r = radius of sphere
Spherical lune r = radius of sphere, θ = dihedral angle
Closed cylinder r = radius of the circular base, h = height of the cylinder
Lateral surface area of a cone s = slant height of the cone,

r = radius of the circular base,
h = height of the cone

Full surface area of a cone s = slant height of the cone,

r = radius of the circular base,
h = height of the cone

Pyramid B = area of base, P = perimeter of base, L = slant height

 Reference:

• Wikipedia Surface Area