The question as it appears in the 08/21 edition of Specs & Techs from GlobalSpec:
We have records that the volume of a pyramid was known by about 1800 BC. Wikipedia speculates that some form of early calculustype of system was used. But the volume of a rectangularbased pyramid can readily be calculated without calculus. How?
(Update: August 28, 8:30 AM) And the Answer is...
Take two pyramids, one with base 'w' x 'd' and
height 'h', the other with all dimensions doubled. The doublesize pyramid
consists of one of the original pyramids, plus a rectangular block w x d x h, plus
four prisms whose joint volume is the same as the volume of the rectangular
block, plus four corner pieces that add up to one singleheight pyramid. So we
can write:
8.Volume = Volume + block + prisms + (bitsofpyramid) = 2.Volume + 2.w.d.h
Solving this gives: Volume = w.d.h/3.
Note 1: that the top does not actually have to be perpendicularly
above a point on the base, because the missing bits can be handled in the same
way; and
Note 2: that people of that time
could have extended the concept to nonrectangular bases, as they already
understood the concept of average areas.

Comments rated to be "almost" Good Answers: