त्रिविमीय आकृतियाँ
3D Shapes
A three-dimensional shape has length, breadth and height. A primary child learns to identify cubes, cuboids, spheres, cylinders and cones around her, and to count their faces, edges and vertices — the standard CTET question on this topic.
Faces, edges and vertices
| Solid | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | 6 | 12 | 8 |
| Cuboid | 6 | 12 | 8 |
| Cylinder | 3 (2 flat, 1 curved) | 2 | 0 |
| Cone | 2 (1 flat, 1 curved) | 1 | 1 (apex) |
| Sphere | 1 curved | 0 | 0 |
| Square pyramid | 5 | 8 | 5 |
| Triangular prism | 5 | 9 | 6 |
Euler's formula: F + V - E = 2 (for solids with flat faces)
Check with a cube: 6 + 8 - 12 = 2. The formula applies to polyhedra, that is solids bounded by flat faces, and not to a cylinder, cone or sphere.
Nets
A net is a flat shape that folds into a solid. A cube has eleven different nets, and identifying which arrangement of six squares folds into a cube is a standard reasoning question. A cylinder's net is two circles and a rectangle; a cone's net is a circle and a sector.
Everyday examples for Classes 1-5
- Cube — dice, a Rubik cube, a sugar cube.
- Cuboid — a brick, a matchbox, a book, a chalk box.
- Cylinder — a water pipe, a tin of ghee, a battery cell.
- Cone — an ice-cream cone, a birthday cap, a heap of grain.
- Sphere — a football, a laddoo, a marble.
Teaching the difference from 2D
Children confuse a circle with a sphere and a square with a cube because textbook pictures of solids are drawn on flat paper. The fix is physical: hand over the real objects, ask children to roll them, stack them and trace their faces. Tracing the face of a cube produces a square, which shows the relationship directly.
✗ A cylinder has 8 edges and 4 vertices. | ✓ A cylinder has 2 edges and no vertices.
✗ Euler's formula works for a cone. | ✓ It applies to solids with flat faces only, not to cones, cylinders or spheres.
संकेत: घन और घनाभ दोनों में 6 फलक, 12 किनारे, 8 शीर्ष; बेलन में कोई शीर्ष नहीं होता।
One or two questions come from 3D shapes, and the face-edge-vertex table answers most of them directly, so memorise it. Cube nets appear as a picture question in many teaching exams, so practise recognising valid ones. The most repeated trap gives a cylinder or cone vertices that they do not have. Another asks which solid is formed by a given net. Euler's formula is asked as a one-liner and its restriction to flat-faced solids is itself a distractor.
Frequently asked questions
How many faces, edges and vertices does a cube have?
A cube has six faces, twelve edges and eight vertices. A cuboid has exactly the same counts; the difference is that a cube's faces are all squares of equal size while a cuboid's are rectangles.
Does a cylinder have vertices?
No. A cylinder has two circular flat faces and one curved surface, meeting in two circular edges, but there is no point where edges meet, so it has no vertices. A cone has exactly one vertex, the apex.
What is a net of a solid?
A flat two-dimensional arrangement of the faces of a solid that can be folded to form it. A cube has eleven distinct nets, and a cylinder's net is made of two circles and one rectangle.
60-second recap
- 3D shapes have length, breadth and height.
- Cube and cuboid: 6 faces, 12 edges, 8 vertices.
- Cylinder: 2 edges, no vertices. Cone: 1 vertex. Sphere: no edge, no vertex.
- Euler's formula F + V - E = 2 applies only to flat-faced solids.
- A net folds into a solid; a cube has eleven nets.