Solution: In the plane ABCD, intersection D is the extension line of DF∨AC intersecting BA at F, connecting A1F.

∠A 1DF is the angle formed by A 1D and AC.

∫ in the rectangle ABCD-a1b1c1d1,AB=AD=2,

∴Rt△A 1AF≌Rt△A 1AD, you can get a1f = a1d.

∵ Two groups of opposite sides of quadrilateral ACDF are parallel respectively.

∴ Quadrilateral ACDF is a parallelogram, and DF=AC=22+22=22 can be obtained.

Let A 1F=A 1D=x,

△A 1DF cos∠A 1DF=8+x2? x22？ 22? X= 10 10，x=25。

Rt△A 1AD，A 1A=A 1D2？ AD2=4

Therefore, the volume of the cuboid ABCD-a1b1c1d1is V = 2× 2× 4 = 16.