Question $1(\backslash (\backslash$mathbf$\{30\}\backslash )$ pts$)$: Consider a thin$-$walled cylindrical tube having a radius of $65$ mm that is to be used to transport pressurized gas. If inside and outside tube pressures are $100$ and $1\mathrm{.}0$ atm $(10\mathrm{.}13$ and $0\mathrm{.}1013$ MPa $),$ respectively,

$($a$)$ compute the minimum required thickness for each of the following metal alloys. Assume a factor of safety of $3\mathrm{.}5.$

$($b$)$ determine a tube constructed of which of the alloys would cost the least amount.