Final answer:
A sphere with an 8 cm diameter has a radius of 4 cm. The possible lengths for the radius of any cross section of this sphere are 2 cm, 3 cm, and 4 cm, as they cannot exceed the sphere's actual radius.
Step-by-step explanation:
The question asks about the possible lengths for the radius of a cross section of a sphere with a diameter of 8 cm. First, to understand the sizes that the radius of any cross section could have, we need to know that the sphere's radius is half of the diameter. Therefore, the radius of the sphere is 4 cm. For any cross sections of the sphere that go through its center, the radius of the cross section will also be 4 cm since it will be equivalent to the radius of the sphere itself.
However, for cross sections that do not go through the center of the sphere, the radius can range from slightly above 0 cm (almost tangent to the sphere) to 4 cm (through the center), but cannot exceed 4 cm. Based on this, the possible lengths for the radius of a cross section of the sphere are 2 cm, 3 cm, and 4 cm as they are all less than or equal to the radius of the sphere.
Therefore, the correct options are 2 cm, 3 cm, and 4 cm.