$(30$ Points$)$ A spherical pressure tank is fabricated using two hemispheres bolted together at the equator. The outside diameter is $d_0=12ft$ and is designed to withstand a pressure of $1800$ psi $.$ If the yield stress is ${}_{\text{y}\text{i}\text{e}\text{l}\text{d}}=36$ksi and a F$.$S$.=2\mathrm{.}0$ is required for safety, determine:

$[$a$]$ the minimum required wall thickness, $t.$

$[$b$]$ The bolts have an ultimate stress ${}_{\text{u}\text{l}\text{t}}=30$ksi. If the bolt diameter is $d=1\mathrm{.}0$ inch, how many bolts are required to securely fasten the two hemispheres?