8th Class Mathematics Visualising Solid Shapes

 Visualising Solid Shapes

• Geometrical shapes:

Plane shapes have two measurements - length and breadth and therefore they are called two-dimensional shapes.

e.g.,

Solid objects have three measurements – length, breadth and height or depth. So, they are called three – dimensional shapes. Also, Solids Occupy some Space.

e.g.,

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• Description of solid shapes:

• Polyhedron:

(i) A solid figure bounded by plane polygonal faces is called a polyhedron.

(ii) The point at which three or more faces of a polyhedron intersect is called a vertex.

(iii) A line along which two faces of a polyhedron intersect is called an edge.

• Regular polyhedron: A polyhedron with regular polygons as its faces is called a regular polyhedron. The same number of faces meet at each vertex.

This polyhedron is regular. Its faces are congruent, regular polygons. Vertices are formed by the same number of faces.

• This polyhedron is not regular. All the sides are congruent; but the vertices are not formed by the same number of faces. We see that three faces meet at A but four faces meet at B.

• Convex polyhedron: A polyhedron in which a line segment connecting any of its two vertices contains only points that are on a face or inside the polyhedron is called a convex polyhedron.

• Prism: A polyhedron with two parallel opposite faces, called bases, that are congruent polygons and the lateral faces are parallelograms is called a prism.

• Pyramid: A polyhedron whose base is a polygon and whose lateral faces are triangles with a common vertex is called a pyramid.

• A prism or a pyramid is named after its base. If a prism has a hexagonal base, it is called a hexagonal prism. A pyramid with a triangular base is called a triangular pyramid.
• Euler's formula for convex polyhedron: For any convex polyhedron, the relation between its faces (F), vertices (V) and edges (E) is given by the following.

F + V = E + 2

• Maps: A map shows the location of a particular object/place in relation to other objects/ places.

(i) We use symbols to depict different objects/places.

(ii) In a map, there is no reference or perspective.

(iii) Maps involve a scale that is fixed for a particular map.

• Different views of 3 - D objects: 3 - D objects appear differently from different positions so they can be drawn from different perspectives.

e.g.,

• Net: The 2 - D figure of a 3-D shape or solid, which when folded gives the solid is called a net.