A student recently asked me why, when solid geometry is taught in school, rectangular prisms and cylinders tend to be heavily emphasized -- and relatedly, why solid-geometry questions on standardized exams (GMAT, GRE) tend to emphasize these shapes.
The most plausible answer I could come up with (on the spot) was twofold:
Convenience: The volumes and surface areas of these figures are relatively simple to calculate, the formulas are intuitive to remember, and they offer a rough-and-ready way to estimate the volume and surface area of more complicated objects.
Relevance: We live in a built environment in which prism-shaped structures (buildings, boxes, furniture) and cylindrical objects or spaces (pipes, wires, tunnels) are common. Knowing how to reason geometrically about these figures is a precursor to solving many engineering problems.
These answers are, I recognize, vague and incomplete, but are they off-base? I realize that both points also apply to cones, spheres, etc.
Moreover, are there other compelling pedagogical reasons that (rectangular) prisms and (right circular) cylinders seem to show up so much in geometry texts and on standardized tests? Or is my belief that they appear "early and often" in geometry pedagogy just a function of spending too much time with the GRE and the GMAT?
Thanks in advance for your help.