3D solids — faces, edges, vertices
OCR J560 begins with naming the parts of a 3D solid and Euler's formula for polyhedra. Beyond Foundation, students apply these to surface area, volume and net problems.
Vocabulary
| Term | Meaning |
|---|---|
| Face | A flat (or curved) surface of the solid. |
| Edge | A line where two faces meet. |
| Vertex (pl. vertices) | A point where edges meet. |
| Net | A 2D layout that folds into the 3D solid. |
Standard solids
| Solid | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | 6 (squares) | 12 | 8 |
| Cuboid | 6 (rectangles) | 12 | 8 |
| Triangular prism | 5 (2 triangles + 3 rectangles) | 9 | 6 |
| Square-based pyramid | 5 (1 square + 4 triangles) | 8 | 5 |
| Tetrahedron | 4 (triangles) | 6 | 4 |
| Cylinder | 3 (2 circles + 1 curved) | 2 (curved) | 0 |
| Cone | 2 (1 circle + 1 curved) | 1 (curved) | 1 (apex) |
| Sphere | 1 (curved) | 0 | 0 |
(For cylinders, cones and spheres, "edges" are sometimes counted as 2, 1, 0 curved edges; OCR accepts either as long as the count is consistent.)
Euler's formula for polyhedra
For any convex polyhedron: F + V − E = 2.
Check: cube → 6 + 8 − 12 = 2 ✓. Tetrahedron → 4 + 4 − 6 = 2 ✓.
Cross-sections and prisms
A prism is a solid with the same cross-section all the way through. The cross-section gives the prism its name (triangular prism, hexagonal prism, etc.). Volume = cross-section area × length.
A pyramid has a polygonal base and triangular faces meeting at an apex.
Nets
Every cube has 11 distinct nets. Foundation J560/01 frequently shows a possible net and asks: does this fold into a cube? Look for: 6 squares, arranged so opposite faces don't share an edge.
For a cuboid: 6 rectangles, 3 pairs of identical opposite faces.
Plans and elevations
A "plan" is the view from directly above. The "front elevation" is the view straight on from the front. "Side elevation" is from the side. OCR J560/03 has used these to test 3D reasoning skills since the spec was rewritten.
OCR mark scheme conventions
- B1 for each correct count (faces, edges, vertices).
- B1 for "applying Euler's formula" if used.
- For nets: B1 for correct shape outline, B1 for correct internal lines/folds.
⚠Common mistakes
- Counting the curved surface of a cylinder as 2 edges instead of 1 (or 0).
- Forgetting the apex when counting vertices of a cone.
- Saying a cuboid has 6 different rectangular faces (it has 3 pairs of identical ones).
- Missing one of the 11 distinct cube nets.
AI-generated · claude-opus-4-7 · v3-ocr-maths-leaves