Just as slicing a cone differently produces a circle, an ellipse, a parabola, or a hyperbola, a cylinder or cube also produces completely different cross-section shapes depending on the cutting angle and position. Pick a shape below and move the angle and position yourself to see how the cross-section changes.
Slice a solid shape cleanly with a knife, and a new flat shape appears where you cut. That's called a cross-section. Even for the same solid, the cross-section shape changes completely depending on the angle and position of the cut.
Depending on the cutting angle, a cone yields a circle, an ellipse, a parabola, and a hyperbola in turn — and these same curves show up in the shape a flashlight beam makes on a wall, and in the shape of a satellite's orbit. The same principle is at work when slicing gimbap or a radish at an angle changes the shape of the cross-section.
Pick a shape, then move the cutting plane's angle and position with the sliders. You can watch the cross-section shape change in real time, depending on how the plane passes through.