A solid circular column has an effective length of $2m$ and an outer diameter of $40mm.$ The engineer wants to reduce the column weight by $25\%$ and replace it with a circular hollow section $($CHS$)$ of the same outer diameter.

Determine;

a$)$ The inner diameter $(x)$ rounded to the nearest whole number in $mm$

b$)$ The percentage reduction in the compression load carrying capacity of the hollow section column

c$)$ The axial compression capacity of the hollow section and the failure mode.

Assume E $=200000$MPa and yield strength $=250$MPa and a factor of safety $1$