I found this in a 1908 Audel's Millwright's Manual.

If you square the diameter of a circle and multiply by .7854, you get
the area of the circle. Also,4 X 0.7854 = Pi. With a little
thought, you can get along without pi, if you want to.

Okay, "So What?" you say.

Well, note that .7854 means that a circle that just fits into its
enscribed square contains 78.54% of the area of that square. And
that's about 80%. So, an easy way to ESTIMATE the area of a circle in
your head is to simply think "8 tenths of the area of the enscribed
square = the area".

Example: A guy offers you a piece of steel just for coming and getting
it off the place RIGHT NOW!
You need to know the approximate weight of a 5" diameter bar of
steel that is 5 feet long, so you can decide whether you will be able to
lift it into your car trunk by yourself.

So, 5 X 5 = 25. 80% of 25 (in your head) is 20. That's area of the
circle. 20 X 60 (5 feet in inches) is 1200. There's the volume of
the bar! That's all there is to it!

Now for the weight:

A cubic inch of steel weighs 0.283 pounds think 2 Ate 3 (cannibalism
of numbers???). 0.283 is about .3

So the bar weighs 1200 X .3 = (in your head) about 360 pounds.
Sorry, Maybe you can lift it, but I'd have to pass on this one!!!

Well, maybe I could------


Pete Stanaitis