Each vertex of the cuboid abcd-a1b1c1d1 is on the sphere of the sphere o with the volume of 32 / 3 Pai, where Aa1 = 2, then the volume of the pyramid o-abcd is smaller The maximum value is

Each vertex of the cuboid abcd-a1b1c1d1 is on the sphere of the sphere o with the volume of 32 / 3 Pai, where Aa1 = 2, then the volume of the pyramid o-abcd is smaller The maximum value is

Let the radius of the ball be r, then (4 / 3) π R & # 179; = (32 / 3) π, and the solution is r = 2, so the diagonal of the cuboid d = 2R = 4, let AB = a, BC = B, because Aa1 = 2, then a & # 178; + B & # 178; + 2 & # 178; = D & # 178; = 16, so a & # 178; + B & # 178; = 12vo ABCD = (1 / 3) ab · (1 / 2) · Aa1 = AB / 3 ≤ (A & # 178