1. **State the problem:** We need to find the maximum working pressure $p$ for a thin spherical steel vessel with diameter $d = 632$ mm, wall thickness $t = 3$ mm, and allowable tensile stress $\sigma = 119$ MPa. 2. **Formula used:** For a thin spherical shell, the hoop stress (tensile stress) is given by $$\sigma = \frac{p d}{4 t}$$ where $p$ is the internal pressure, $d$ is the diameter, and $t$ is the wall thickness. 3. **Rearrange the formula to solve for $p$:** $$p = \frac{4 t \sigma}{d}$$ 4. **Substitute the given values:** $$p = \frac{4 \times 3 \times 119}{632}$$ 5. **Calculate the numerator:** $$4 \times 3 \times 119 = 1428$$ 6. **Calculate the pressure:** $$p = \frac{1428}{632} \approx 2.26$$ 7. **Interpretation:** The maximum working pressure the vessel can safely withstand is approximately $2.26$ MPa. **Final answer:** $$\boxed{2.26 \text{ MPa}}$$