A very old steel pole vault pole has been examined by material scientists studying properties of steel. According to the oldest

Olympic pole$-$vault coach alive, the pole was required to support a tensile force of $3k$ in order to be effective. The wall thickness of the pole is $0\mathrm{.}1in.$

a$)$ Find the minimum required outer diameter if the allowable tensile stress when someone vaulted was $12,000$ psi? $($Round to $3$ decimal places$)$

$d_{\text{m}\text{i}\text{n}}=$

b$)$ Back in the day someone sabotaged the world record vaulter and drilled a hole in the middle of their steel pole that was $\frac{1}{10}$ the size of the outer diameter. Luckily the vaulter was not injured and continued to break records. Repeat part $($a$)$ taking the hole into consideration. $($Round to $3$ decimal places$)$

$d_{\text{m}\text{i}\text{n}}=$

in$.$