(Ⅰ)证明:∵EA⊥平面ABC,FC∥EA,∴FC⊥平面ABC∵AB?平面ABC∴FC⊥AB又∵AC是直径,B在圆上,∴AB⊥BC∴AB⊥平面BFC又∵BF?平面BFC∴AB⊥BF.(Ⅱ)在△ABC中,∠BAC=30°,BM⊥AC交AC于点M,AC=4,∴BM= 3 ,三角形EMF的面积S= 1 2 (3+1)×4? 1 2 ×3×3? 1 2 ×1×1=3VE-BMF=VB-EMF= 1 3 ×3× 3 = 3 .