Math CentralQuandaries & Queries


Question from Juanita, a parent:

What is the relationship between the volume of a prism and a pyramid
with congruent base areas and heights?

Hello Juanita,

There are many varieties of prisms and pyramids.
Check out these links,

If your prism is a 'right' prism and your pyramid is a 'triangular' pyramid, then their volume formulae are, respectively: V = Ah, and V = (1/3)Ah where 'A' is the area of the base and 'h' is the height.

If the bases areas and heights are congruent (i.e. "the same"), then the volume of the pyramid is 1/3 the volume of the prism. If you have different types of prisms or pyramids, the relationship between them may be different.


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