三棱柱ABC-A1B1C1中,侧面AA1B1B⊥底面ABC,直线A1C与底面成60°角,AB=BC=CA=2,AA1=A1B,则该棱柱的体积为_.

问题描述:

三棱柱ABC-A1B1C1中,侧面AA1B1B⊥底面ABC,直线A1C与底面成60°角,AB=BC=CA=2,AA1=A1B,则该棱柱的体积为______.

取AB的中点D,连接A1D,CD,∵AB=BC=CA=2,AA1=A1B,∴A1D⊥AB,CD⊥AB,∵直线A1C与底面成60°角,∴∠A1CD=60°,CD=3,CA1=23,A1D=3,A1D是三棱柱ABC-A1B1C1的高,∴S△ABC=12×AB×CD=3.∴该棱柱的体积V=S△...