Geometry: 3-D Measurements
Volume
Volume for three-dimensional figures is the equivalent of area for two-dimensional figures. Volume is a three-dimensional measurement; that is, it measures the combined length, width, and height of a figure. Because planes, polygons, and other two-dimensional figures don't have height, they have no volume. Only solids and figures with dimension greater than or equal to three have volume.
The unit for volume is the cubic unit. Liquid medicine is often measured in cubic centimeters, whereas a swimming pool full of water may be measured in cubic feet. One cubic unit is a cube with edges of length one. It looks something like this:
Naturally, very few solids break down nicely into components of cubic units. But just as polygons can be divided into triangles, polyhedra can be divided into pyramids, and the volume of a pyramid is possible to calculate. In the next lesson, we'll study the ways to calculate the volume of polyhedra as well as spheres.
