$\varepsilon = \dfrac{\sigma_x}{E} - \nu \dfrac{\sigma_y}{E} = 0$
$\sigma_x = \nu \, \sigma_y = \sigma_l$ → longitudinal stress
$\sigma_t = \sigma_y$ → tangential stress
$\sigma_t = \dfrac{pD}{2t} = \dfrac{6000(3)}{2(0.10)}$
$\sigma_t = 90\,000 \, \text{ psi}$ answer
$\sigma_l = \nu \, \sigma_y = \frac{1}{3} (90\,000)$
$\sigma_l = 30\,000 \, \text{ psi}$ answer