take a 3-dimensional object, and picture a sharp knife cutting it.
More correctly, a "plane" (thus, 2-dimensional) going through it.
The point at which the knife - or plane - intersects or touches the 3D object, is its cross section.
In a simple case, for example a sphere (meaning a "ball" with no middle, only a surface) then ANY cross section of it will be a "circle", (if you are "just touching it" you'd have a point, which is -- sort of like a circle of 0 radius).
That is the geometric definition.
A "practical" definition might be the "cross section of an airplane body". In THIS case your cross section would show the outer skin, the frame, the inner wall, the seats, floor, air ducts, wiring, hydraulic lines (which would look like 'o' because you presumably sliced it perpendicular to the way it is going), etc. Thus a computer aided design or drafting (CAD) program could show you a "slice" of something - a cross section - at any point, to for example see how close something is to something else, etc.
Another cross-section example would be CAT scans - such as for a brain problem - each computer generated slice is a "cross section" of the brain at that distance say from the top of your head (though it could be shown front to back, or probably any angle) - but what you are seeing is the intersection of a "plane" and the object.
Cross-section of a trough, a wheelbarrow, some rooves.
The shape that emerges from a perpendicular cross-section depends on the original three-dimensional object being cut. For example, if you cross-section a cylinder perpendicularly, you will get a circle. If you do the same with a cube, the resulting cross-section will be a square. Each geometric shape produces a unique two-dimensional shape when intersected in this manner.
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 cylinder has a circular cross section that is parallel to its base.
A cross section of a polyhedron is formed by slicing the polyhedron with a plane, which can intersect the faces, edges, and vertices in various ways. Depending on the angle and position of the slicing plane, the resulting cross section can produce shapes that differ significantly from the base of the polyhedron. For example, slicing a rectangular prism diagonally can yield a triangular cross section, illustrating how the orientation of the cut affects the shape. Thus, the cross section may not necessarily match the base due to these factors.
Yes a prism can have a square cross-section
Cross-section of a trough, a wheelbarrow, some rooves.
Yes. A cuboid, for example, has triangular cross sections
The shape that emerges from a perpendicular cross-section depends on the original three-dimensional object being cut. For example, if you cross-section a cylinder perpendicularly, you will get a circle. If you do the same with a cube, the resulting cross-section will be a square. Each geometric shape produces a unique two-dimensional shape when intersected in this manner.
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 cylinder has a circular cross section that is parallel to its base.
Not a right cross-section.
cross-section of a root
A cross section of a polyhedron is formed by slicing the polyhedron with a plane, which can intersect the faces, edges, and vertices in various ways. Depending on the angle and position of the slicing plane, the resulting cross section can produce shapes that differ significantly from the base of the polyhedron. For example, slicing a rectangular prism diagonally can yield a triangular cross section, illustrating how the orientation of the cut affects the shape. Thus, the cross section may not necessarily match the base due to these factors.
trapezoidal cross section
Every cross-section of a sphere is a circle.
No, a cube cannot have an octagonal cross-section.