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Solid Geometry

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 $\ell$ of one of its 8 edges: $V = \ell\,^3$. 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


  
Figure: Triangular, square and circular right cylinders.
\begin{figure}
\begin{center}\mbox{
\epsfig{file=PS/cylinders.ps,height=2.5in} }\end{center}\end{figure}


next up previous
Next: Algebra 1 Up: Geometry Previous: The Pythagorean Theorem:
Jess H. Brewer - Last modified: Fri Nov 13 16:16:50 PST 2015