1、∵AD⊥AB且AD⊥AA1∴AD⊥面AA1B1B∴AD⊥AE∵AD‖A1D1∴AE⊥A1D1∵AB=BE=EB1=A1B1=1,∠ABE=∠A1B1E=90o∴∠AEB=∠A1EB1=45o∴∠AEA1=90o即AE⊥A1E由AE⊥A1D1&AE⊥A1E∴AE⊥面A1D1E2、连接BC1,过E作BC1垂线,垂足为点F∵C1D1⊥面BB1DC1C∴EF⊥C1D1由EF⊥C1D1&EF⊥BC1∴EF⊥面ABC1D1∴EF⊥面AC1D1∵△BEF∽△BC1B1∴EF/BE=B1C1/BC∴EF=根号5/5∵△AC1D1面积=1/2*C1D1*AD1=根号5/2∴三棱锥E-AC1D1的体积V=1/3*S*h=1/6