3. In a transparent sealed cubic container, there is exactly half the volume of the container filled with water. When the cubic container is rotated arbitrarily, the shape of the water surface in the container can be:
(1) triangle, (2) rhombus, (3) rectangle, (4) square, (5) regular hexagon.
The correct conclusion is:
Pick one
3.C.
The problem is transformed into determining the cross-sectional shape of a cube, and this cross-section divides the cube's volume equally. Clearly, the sections that meet the requirements are (3) and (4). The cross-section is a rhombus, as shown in Figure 1; the cross-section is a regular hexagon, as shown in Figure 2. In Figure 1, and are the midpoints of and , respectively. In Figure 2, , , , , , and are the midpoints of the edges, respectively.