pyramid and cuboid

Why the pyramid is 1/3 of cuboid?

Presumably, what you mean to say is that the volume of a rectangular-based pyramid is 1/3 of the volume of a cuboid with the same base and the same height. That is a lot to leave out of a question!

This can be proved in several ways, some of which are more general: The volume of any pyramid is 1/3 of the volume of the prism with the same base and height.

If I were you, I would go to Google and enter "prove volume of pyramid"; you will find various video or written explanations, and can look among them for one that satisfies you. We don't know what kind of proof you will understand. (Calculus? infinite series? a series of proofs in Euclidean geometry?)

Here is a long, detailed version of the infinite series proof: http://pythagoreanmath.com/deriving-the-volume-of-a-pyramid/

Here is Euclid's proof: https://mathcs.clarku.edu/~djoyce/java/elements/bookXII/propXII7.html

Here is an informal discussion, with links to other approaches: http://mathforum.org/library/drmath/view/66972.html

Here is a similar visual approach: https://nrich.maths.org/1408
 
Presumably, what you mean to say is that the volume of a rectangular-based pyramid is 1/3 of the volume of a cuboid with the same base and the same height. That is a lot to leave out of a question!
Thanks!!!!
 
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