Important Formulae: Solids | Mathematics & Pedagogy Paper 1 for CTET & TET Exams - CTET & State TET PDF Download

Types of Solids

• Cubes and Cuboids: Examples include dice, boxes, and bricks. They have 6 faces, 12 edges, and 8 vertices.
• Spheres: Examples include balls and globes. Spheres have 1 curved surface and no edges or vertices.
• Cylinders: Examples include cans and pipes. Cylinders have 3 surfaces (2 flat, 1 curved), 2 edges, and 0 vertices.
• Cones: Examples include ice cream cones and traffic cones. Cones have 2 surfaces (1 flat, 1 curved), 1 edge, and 1 vertex.
• Pyramids: Examples include Egyptian pyramids and certain roofs. Pyramids have a polygonal base and triangular faces meeting at a vertex.

Faces, Edges, and Vertices

• A face is a flat surface.
• An edge is where two faces meet.
• A vertex is a point where two or more edges meet.
• Counts for Shapes:
  • Cube and Cuboid: 6 faces, 12 edges, 8 vertices.
  • Cylinder: 3 faces (2 flat, 1 curved), 2 edges, 0 vertices.
  • Cone: 2 faces (1 flat, 1 curved), 1 edge, 1 vertex.
  • Sphere: 1 curved surface, 0 edges, 0 vertices.

Nets

• A net is a 2D figure that can be folded into a 3D object.
• Example: The net of a cube consists of 6 squares that can be folded into a cube.
• Example: Different nets can be folded to form a cylinder or cone.

Views of 3D Shapes

• 3D shapes can be viewed from the top (Plan), front (Front Elevation), and side (Side Elevation).
• Example: Different views of a car show how 3D shapes can be represented in 2D.

Symmetry

• Reflection Symmetry: A figure and its mirror image are exactly symmetrical.
• Planes of Symmetry: Divide a 3D shape into two congruent shapes.
• Rotational Symmetry: A shape fits into itself after a certain rotation. Example: A square has rotational symmetry of order 4.