source: ncert
topic: geometry
class_level: class_8
chapter: ch10
difficulty: beginner
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.