The truncated square pyramid is a special case of a pyramidal frustum for a square pyramid. Let the base
and top side lengths of the truncated
pyramid be 
and 
,
and let the height be 
. Then the volume of the solid is
 |
Problem 14 of the Moscow Mathematical Papyrus, dating to about 1850 BC, applies this formula with 
,
,
and 
to obtain the correct volume 
(History of Mathematics Project). The Egyptians cannot
have proved it without calculus, however, since Dehn
showed in 1900 that no proof of this equation
exists which does not rely on the concept of continuity
(and therefore some form of integration).
