you can try h' = 0.707*h and a' = 0.707*a
A classic pyramid with square footprint, hight h, sidelength a and volume V.
Like seen, eg. in Square Pyramid Calculator
Assume it is a hollow container, with infinitively thin walls. It's filled with a volume of water = V/2, ie, it is half full (by volume). How far up from the bottom would the water reach, expressed in units of h, ie. How deep will the water be inside the pyramid, compared to the total hight of the pyramid.
Can this be solved in general, ie. Without knowing any specific values of h and a? Is the depth of water always a specific (constant) fraction of h. Or is the answer depending on the slant angle of the pyramid surface?
For completeness. The original question mentions specific values of h and a, I can't remember the values, but lets say h=300m and a=200m, though this is of cause not relevant for my question...
2. The volume of the pyramid is calculated by:
You are looking for a pyramid with with a' as the sidelength of the square and h' as the height of the smaller pyramid.
3. Use proportion:
4. Now you know:
5. Plug in this value into the equation of #3 to determine the value of a'.
Having looked closer on your calculations... I can follow you clearly as far as 3., but in 4. I get confused.