For a sphere with a radius of 2, ABCD tetrahedron has four points on the sphere, AB=CD=2, and find the maximum volume.

Triangle ABO and CDO are equilateral triangles,

The largest volume should be AB vertical CD, and the midpoint line between AB and CD should pass through the center of the ball.

The midpoint of CD is E, the ABE area is 2√3, the height is 2, and the volume is 4√3/3.

Choose B.