SEARCH HOME
 Math Central Quandaries & Queries
 Question Shaheer: Do a three sided pyramid and a square pyramid have the same formula if you want to calculate the volume?

Hi,

If you mean

$\mbox{Volume = } \frac13 \mbox{ (area of the base) }\times \mbox{ (the height)}$

then the answer is yes. In fact the apex of the pyramid does not need to be above the center of the base, so the pyramid can be leaning, as long as the height is the perpendicular distance from the plane containing to base to the apex.

This follows from a much more general result that says

if you take some region R in the plane with an area, some point V not in the plane and form a cone by joining every point on the boundary of R to V with a straight line then the volume of the cone is

$\frac13 \mbox{ (area of the base) }\times \mbox{ (the height)}$

Penny