Surfacearea

Surface area is the measure of the total area that the surface of a three-dimensional object occupies. It is the sum of the areas of all exposed surfaces. In objects with curved surfaces, the term often refers to the curved surface area, while the total surface area includes both curved and flat faces. Surface area is expressed in square units, such as square meters (m^2) or square centimeters (cm^2).

Formulas for common shapes:

Cube with edge length a has SA = 6a^2. Rectangular prism with edges l, w, h has SA = 2(lw + lh + wh). Sphere of radius r has SA = 4πr^2. Cylinder with radius r and height h has SA = 2πr(h + r). Cone with radius r and slant height l has total SA = πr(l + r) (including base). The curved surface area is πrl for a cone and 2πrh for a cylinder, with base areas added to obtain the total.

For irregular shapes, surface area can be found by decomposing into simpler components or using integral calculus.

Applications of surface area include estimating material requirements for coatings, paint, plating, or construction, and modeling the surfaces of cells or other objects in science.