Cross-Sections of 3D Solids Explorer
Interactive tool for Common Core G-GMD.4. Pick a solid and a cutting plane to see the 2D cross-section it forms, with a rotatable 3D view and the named shape.
Drag to rotate the solid. The amber plane is the cut.
Cross-section
Cylinder cut horizontal
A horizontal slice perpendicular to the axis of a cylinder gives a circle.
What a cross-section is
A cross-section is the 2D shape you get when a flat plane slices through a 3D solid. The plane meets the solid along a flat region, and the boundary of that region is the cross-section. Slicing an orange gives a circle. Slicing a loaf of bread gives a rectangle.
How orientation changes the shape
The same solid can produce different cross-sections depending on how the plane is tilted. A cylinder gives a circle when cut horizontally, a rectangle when cut straight down through its axis, and an ellipse when cut at an angle. Rotate the 3D view and move the plane to see this for each solid.
Standard G-GMD.4
Common Core HSG-GMD.A.4 asks students to identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. This tool focuses on the slicing direction so students build a clear mental model of each result.
Common results
| Solid | Horizontal | Vertical | Angled |
|---|---|---|---|
| Cube | Square | Square | Rectangle |
| Cylinder | Circle | Rectangle | Ellipse |
| Cone | Circle | Triangle | Ellipse |
| Square pyramid | Square | Triangle | Trapezoid |
| Sphere | Circle | Circle | Circle |
| Triangular prism | Triangle | Rectangle | Rectangle |
