Good engineering and science students at good universities have memorized
the formulas C = 2*pi*R and A = pi*R^2 but often do not know which applies
when to what, nor that there is any connection to things they really do
know. It would be awfully useful somewhere to start with the circumference
being about 4*(2R) = 8R (the circumference of the bounding square) and then
see that this is only a bit bigger than 2*pi*R, and to start with the area
being about (2R)^2 = 4R^2 (the area of the bounding square) and then see
that this is only a bit bigger than pi*R^2.
An example of confusion is the frequently seen A = 2pi*R^2.