Current Affairs 8th Class

Visualising Solid Shapes

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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.,

Description of solid shapes:

S.NO.	Solid Shape	Number of Vertices	Number of edges	Number of faces
1.	Cube	8	12	6
2.	Cuboid	8	12	6
3.	Cone	1	1 Curved edge	1 Curved face, 1 flat face
4.	Cylinder	Nil	2 Curved edges	2 flat face 1 Curved face
5.	Sphere	Nil	Nil	1 Curved face

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.

Algebraic Expressions and Identities

Mensuration

Current Affairs 8th Class

Visualising Solid Shapes

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