Round
The shape of the cross section depends on the 3D object being sliced. For example, if you slice through a cylinder horizontally, the cross section would be a circle. If you cut through a cube diagonally, the cross section could be a triangle or a rectangle, depending on the angle of the cut. Thus, the specific 2D shape observed in the cross section varies based on the object's geometry and the orientation of the cut.
a square
an oval hemispere * * * * * The cross section must be 2-dimensional so it cannot be a hemispere - or hemisphere, even. I suggest the shape is lenticular: the shape of a convex lens (with equal radii of curvature).
The horizontal cross-section of a pyramid forms a square when the pyramid has a square base and is sliced parallel to that base. This is because all points on the cross-section are equidistant from the center of the base, maintaining the same proportions as the base itself. As the cut is made at any height, the resulting shape remains a square, regardless of the height of the slice. If the pyramid's base were a different shape, the cross-section would reflect that shape instead.
My $210 Physical Geography class text book does not have the answer. It just says it would be smaller than the diameter of a cross section through the equator.
A cross section of Earth cut from pole to pole would reveal a roughly circular shape. This is because Earth is an oblate spheroid, meaning it is slightly flattened at the poles and bulging at the equator due to its rotation.
Imagine that you wanted to cut a globe or a sphere exactly in half. When you looked at the cut you would see an exact circle on both pieces. This area would be the cross-section. You could work out the area of this cross-section by using A = Pi X r squared. But be careful. Don't assume that the cross sectional area is the same no matter where you cut. If you cut the globe at some other point, say near to the edge, the cross-section (the circular area that you would see) would be a lot smaller. You would come across a uniform cross-section if you cut a cable. No matter where you cut the cable the cross-section should be roughly the same. Also cross section doesn't have to be circular. The cross-section you get really depends on the original shape you are dealing with. If you cut a cube in half, you would get a square cross-section. So I guess you could imagine the term as applying to cutting across (hence cross) something to reveal 2 sections (hence section).
A square cross-section cuboid would fit the given description
An hexagonal cross-section prism would fit the given description.
The horizontal cross section of a Coke can or bottle typically reveals a circular shape. This circular cross section represents the volume of the liquid inside, which is uniform in density and composition. If you were to look at the surface of the liquid, it would appear flat, reflecting the curvature of the container's sides.
The cross-section of a rectangular pyramid sliced by a plane will typically result in a polygonal shape. If the cutting plane is parallel to the base of the pyramid, the cross-section will be a smaller rectangle. If the plane intersects the sides at an angle, the resulting cross-section may be a trapezoid or a triangle, depending on the height at which the slice occurs. The specific shape can be described by points W, X, Y, and Z, which would represent the vertices of the cross-section.
A basketball is a sphere so a cross-section would be a circle.