- A SKEPTICs GUIDE - A SKEPTICs GUIDE 
Most of us learned how to calculate the volumes
of various solid or 3-dimensional objects even before we
were told that the name for the system of conventions and
``laws'' governing such topics was ``Solid Geometry.''
For instance, there is the cube, whose volume V
is the cube (same chicken/egg problem again)
of the length 
of one of its 8 edges:
.
Similarly, a cylinder has a volume V equal to
the product of its cross-sectional area A and its
height h perpendicular to the base:
V = Ah. Note that this works just as well for any shape
of the cross-section - square, rectangle, triangle, circle or even
some irregular oddball shape.
If you were fairly advanced in High School math, you probably learned a bit more abstract or general stuff about solids. But the really deep understanding that (I hope) you brought away with you was an awareness of the qualitative difference between 1-dimensional lengths, 2-dimensional areas and 3-dimensional volumes. This awareness can be amazingly powerful even without any ``hairy Math details'' if you consider what it implies about how these things change with scale.4.4
