A thin-walled cylindrical pressure vessel is constructed using an alloy for which Kc = 50 MPa Vm and oy = 1000 MPa. The pressure vessel has a diameter d = 2r = 3 m and wall thickness, t, of 30 mm and is known to have thumb-nail cracks of depth 10 mm oriented perpendicular to the hoop stress direction. The vessel is subjected to an increasing internal pressure for which the hoop stress is given by pr 00 t. The stress intensity factor for the thumb-nail cracks is given by K = 1.260a (where a is the crack depth). (a) How will the pressure vessel fail? Please provide necessary solution steps.