Cross-sectional area

Area and volume

The cross-sectional area (${\displaystyle A'}$) of an object when viewed from a particular angle is the total area of the orthographic projection of the object from that angle. For example, a cylinder of height h and radius r has ${\displaystyle A'=\pi r^{2}}$ when viewed along its central axis, and ${\displaystyle A'=2rh}$ when viewed from an orthogonal direction. A sphere of radius r has ${\displaystyle A'=\pi r^{2}}$ when viewed from any angle. More generically, ${\displaystyle A'}$ can be calculated by evaluating the following surface integral: