| --- |
| source: ncert |
| topic: geometry |
| class_level: class_8 |
| chapter: ch10 |
| difficulty: beginner |
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| |
| Class 8 | Ch10: Visualising Solid Shapes |
| VIEWS OF 3D OBJECTS: |
| Front view, Side view (left or right), Top view (plan view). |
| Different views give 2D shapes from different angles. |
| Cube: all views are squares. |
| Cuboid: views are rectangles (different dimensions for different views). |
| Cylinder: front/side=rectangle, top=circle. |
| Cone: front/side=triangle, top=circle with centre point. |
| Sphere: all views are circles. |
| MAPPING AND SCALE: |
| Map is a scale drawing of a region. |
| Scale: 1cm represents actual distance. Scale 1:50000 means 1cm=50000cm=500m. |
| Distance on map × scale = actual distance. |
| POLYHEDRA: |
| Polyhedron: solid with flat faces, all faces are polygons. |
| Regular polyhedra (Platonic solids): all faces identical regular polygons. |
| Tetrahedron: 4 equilateral triangular faces. |
| Cube: 6 square faces. |
| Octahedron: 8 equilateral triangular faces. |
| Dodecahedron: 12 regular pentagonal faces. |
| Icosahedron: 20 equilateral triangular faces. |
| Euler's formula: F+V-E=2 for all polyhedra. |
| NON-POLYHEDRA: cone, cylinder, sphere (have curved surfaces). |
| SOLVED EXAMPLES: |
| Example 1: Top view of a cone is a circle with a point (apex) at centre. |
| Example 2: Map scale 1:50000. Distance on map=3cm. Actual distance=3×50000cm=1.5km. |
| Example 3: Verify Euler: Octahedron F=8,V=6,E=12. F+V-E=8+6-12=2. Correct. |
| COMMON MISTAKES: |
| Cylinder and cone are NOT polyhedra (have curved surfaces). |
| Top view of cone shows circle with a dot in centre, not just a circle. |
