A vertical slender structure of variable cross-sectional area A(z) must be shaped such that the compressive stress at every level is the same. The base area A 0 and the height H are specified. Assume...

A vertical slender structure of variable cross-sectional area A(z) must be shaped such that the compressive stress at every level is the same. The base area A₀
and the height H are specified. Assume that the structure is solid with the density 𝜌. Determine the shape A(z), the top cross-sectional area A_H, the volume of the structure, and the weight of the superstructure that is supported by A_H.