| --- |
| source: ncert |
| topic: geometry |
| class_level: class_7 |
| chapter: ch15 |
| difficulty: beginner |
| --- |
| |
| Class 7 | Ch15: Visualising Solid Shapes |
| 3D shapes (F=faces, E=edges, V=vertices): |
| Cube: F=6,E=12,V=8. Cuboid: F=6,E=12,V=8. Triangular prism: F=5,E=9,V=6. |
| Square pyramid: F=5,E=8,V=5. Tetrahedron: F=4,E=6,V=4. |
| Cylinder: F=3(2 circles+1 curved),E=2 curved,V=0. Cone: F=2,E=1,V=1(apex). Sphere: F=1,E=0,V=0. |
| Euler's formula for polyhedra: F+V-E=2. Cylinder/cone/sphere NOT polyhedra. |
| Cube: F+V-E=6+8-12=2. Tetrahedron: 4+4-6=2. Triangular prism: 5+6-9=2. |
| Nets: 2D folded into 3D. Cube has exactly 11 valid nets. |
| Views: Cylinder→front=rectangle, top=circle. Cone→front=triangle, top=circle with point. |
| Cross-section: cube horizontal=square. Cone through apex=triangle. Cone parallel to base=circle. |
| Cylinder has 3 faces not 2. Cube has 12 edges (4 top+4 bottom+4 vertical). |
