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Given is a pyramid with height h and baselines a and b.

Now imagine we want to construct the volume of the outerbody, i.e. cuboids stacked on each other, in those the whole pyramide is in - or the innerbody, i.e. cuboids stacked on each other which are entirely in the pyramid.

The question is what the volume of these inner- and outerbody is, given that the height of each cuboid is $\frac{h}{4}$.

According to my solutions it is the following for the outerbody:

(a*b)*h/4+(3/4a+3/4b)*h/4 + (a/2*b/2)*h/4+(a/4*b/4)*h/4

And the following for the innerbody:

(3/4a*3/4b)*h/4+(a/2*b/2)*h/4+(a/4*b/4)*h/4

How does one come up with these formulae and how do I know that for the innersum there is only space for three (instead of the four for the outersum) cuboids?

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