- A SKEPTIC's GUIDE - A SKEPTIC's 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
