A square.
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a rectangle.
circle just did it on apex
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).
No, a prism has flat sides. Triangular prisms are very common, but any polygon can be the cross section of a prism.
A cross section of a cylinder along its length is called a rectangle. When a cylinder is cut along its length, the resulting shape is a rectangle with a length equal to the circumference of the cylinder and a height equal to the height of the cylinder. The area of this rectangle represents the lateral surface area of the cylinder.