A hollow shaft of diameter ratio 3/8 is required to transmit 500 kW at 110 r.p.m., the maximum torque being 20% greater than the mean. The shear stress in not to exceed 60 N/mm2 and the twist in a length of 3 m not to exceed 1.4 degrees. Calculate the maximum external diameter satisfying these conditions. Take C = 84 kN/mm2.