a fixed value of one of the variables is a conditional density function of the other variable (conditional on the fixed value defining the plane section). If instead the plane section is taken for a fixed value of the density, the result is an iso-density contour. For the normal distribution, these contours are ellipses. In economics, a production function specifies the output that can be produced by various quantities and of inputs, typically labor and physical capital. The production function of a firm or a society can be plotted in three-dimensional space. If a plane section is taken parallel to the -plane, the result is an isoquant showing the various combinations of labor and capital usage that would result in the level of output given by the height of the plane section. Alternatively, if a plane section of the production function is taken at a fixed level of —that is, parallel to the -plane—then the result is a two-dimensional graph showing how much output can be produced at each of various values of usage of one input combined with the fixed value of the other input . Also in economics, a cardinal or ordinal utility function gives the degree of satisfaction of a consumer obtained by consuming quantities and of two goods. If a plane section of the utility function is taken at a given height (level of utility), the two-dimensional result is an indifference curve showing various alternative combinations of consumed amounts and of the two goods all of which give the specified level of utility. Area and volume Cavalieri's principle states that solids with corresponding cross-sections of equal areas have equal volumes. The cross-sectional area () 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 when viewed along its central axis, and when viewed from an orthogonal direction. A sphere of radius r has when viewed from any angle. More generically, can be calculated by evaluating the following surface integral: where is the unit vector pointing along the viewing direction toward the viewer, is a surface element with an outward-pointing normal, and the integral is taken only over the top-most surface, that part of the surface that is "visible" from the perspective of the viewer. For a convex body, each ray through the