In Geometry 1, we were introduced to the idea of
three-dimensional surfaces. We chiefly studied simple
closed surfaces and, more specifically,
polyhedrons. Remember, polyhedrons are
surfaces made up entirely of polygons. The surfaces we studied rarely exist
alone in the world--they are usually united with their interior points to form a
three-dimensional solid, like a ball of clay, for example. Three-dimensional
solids have measurements analogous to perimeter
and area; they are called surface
area and
volume. Where perimeter is a measure of length only--it
is a one-
dimensional measure for figures of two dimensions--surface area is a measure
solely of area, a two-dimensional measure of solids that exist in three
dimensions. Both surfaces and solids have surface area. The surface area of a
solid is simply the area of the surface that encloses it.

Solids also have volume, the three-dimensional equivalent of area. The most
prevalent way to compare solids is by their volume. In the following lessons
we'll discuss the volume of such surfaces as
cylinders,
cones, and
spheres. In reality, these surfaces have
no volume because they are two-dimensional, but here we'll refer to the solids
which they bound as the surfaces themselves. For example, we'll call the solid
bound by a prism a prism, the solid bound by a cone a cone. This way, when we
learn about volume, we don't need to keep saying, "the volume of the solid bound
by a..."

The reason for this lengthy explanation is that keeping track of dimension is
one of the most important tasks of a geometry student, and you should never fall
into the trap of thinking that certain objects have more dimensions than they
really have. So remember that surfaces like prisms and pyramids are
two-dimensional, even though in this section we'll use their names to denote the
solids that they bound in an effort to explain volume without extra language.