A thick$-$walled pipe with $0\mathrm{.}4$ m inside diameter and $0\mathrm{.}1$ m wall thickness is mad from a material whose ultimate strength is $250$ MPa $.$ If $v=0\mathrm{.}3$ and $E=197$GPa., determine

a$)$ for $P_0=0,$ the maximum internal pressure to which the cylinder may be subjected without exceeding the ultimate strength,

b$)$ for $P_i=0,$ the maximum external pressure to which the cylinder can be subjected without exceeding the ultimate strength, and

c$)$ the radial displacement of a point on the inner surface for case $($a$).$