1. I assume that the material of the pyramid is homogenous. Then the weight correspond directly to the volume:
where k is a real constant.
2. denotes the base area of the complete pyramide, b the base area of the smaller pyramide. Both areas are similar. Then
with
3. h denotes the height of the smaller pyramid. Then the volume is calculated by:
with
4. Since and are similar you can use the proportion:
5. Plug in this term into the equation at #3:
Solve for h.