Answer
(a) The compressive stress at the bottom of the column is $\rho g h$
(b) The maximum height of a column is $7.6~km$
(c) This maximum height should not be a practical concern since we don't construct buildings with a height of $7.6~km$.
Work Step by Step
(a) We can find mass of the column:
$m = \rho~V$
$m = \rho~\pi~r^2~h$
We can find the compressive stress at the bottom of the column:
$Stress = \frac{F}{A}$
$Stress = \frac{mg}{\pi~r^2}$
$Stress = \frac{\rho~\pi~r^2~h~g}{\pi~r^2}$
$Stress = \rho g h$
The compressive stress at the bottom of the column is $\rho g h$
(b) We can find the maximum height of a column:
$\rho~h~g = 2.0\times 10^8~Pa$
$h = \frac{2.0\times 10^8~Pa}{\rho~g}$
$h = \frac{2.0\times 10^8~Pa}{(2700~kg/m^3)(9.80~m/s^2)}$
$h = 7600~m$
$h = 7.6~km$
The maximum height of a column is $7.6~km$
(c) This maximum height should not be a practical concern since we don't construct buildings with a height of $7.6~km$.
