(2012•武昌区模拟)如图,已知四棱台ABCD-A1B1C1D1的侧棱AA1垂直于底面ABCD,底面ABCD是边长为2
(2012•武昌区模拟)如图,已知四棱台ABCD-A
1B
1C
1D
1的侧棱AA
1垂直于底面ABCD,底面ABCD是边长为2的正方形,四边形A
1B
1C
1D
1是边长为1的正方形,DD
1=2.
( I)求证:平面A
1ACC
1⊥平面B
1BDD
1;
(Ⅱ)求四棱台ABCD-A
1B
1C
1D
1的体积;
(Ⅲ)求二面角B-C
1C-D的余弦值.