Visualising Solid Shapes

Notes of chapter: Visualising Solid Shapes are presented below. Indepth notes along with worksheets and NCERT Solutions for Class 8.

(1) Two dimensional figure-

The figure which has only two dimensions, i.e., length and breadth is known as two dimensional figure. We can write it as 2-D.These 2-D figures are also called plane figures.

Eg: – Rectangle, square, triangle etc.

 

Rectangle: Two Dimensional Figure of NCERT Chapter Visualising Solid Shapes          Square: Two Dimensional Figure of NCERT Chapter Visualising Solid Shapes

                Rectangle                                                         Square

 

(2)Three dimensional figure-

The figure which has three dimensions, i.e., length, breadth and height is known as three dimensional figure. We can write it as 3-D.These 3-D figures are also called solid figures.

Eg:- Cuboid, cube, cone etc.

 

Cuboid: Three Dimensional Figure of NCERT Chapter Visualising Solid Shapes         Cube: Three Dimensional Figure of NCERT Chapter Visualising Solid Shapes

                 Cuboid                                                                           Cube

(3) Parts of 3-D figure-

(i)Vertices-

A point where two or more lines, curves and faces of a solid figure meet is known as vertices.  In simple words, corners of any figure are known as vertices.

Eg:-

 

Vertex of NCERT Chapter Visualising Solid Shapes

Vertex is singular form of vertices.

A cube has 8 corners or vertices.

(ii) Edges-

The line segments which join vertices and faces of 3D figures are known as edges.

Eg:-

 

Edges of NCERT Chapter Visualising Solid Shapes

A cube has 12 edges.

(iii) Faces-

The flat surfaces of 3-D figures are known as faces.

Eg:-

 

Faces of NCERT Chapter Visualising Solid Shapes

A cube has 6 faces.

In above figure-

ABCD, DCHE, ADEF, BCHG, EFGH and ABFG are faces of a cube.

(4)Net-

A 2-D outline of a solid or 3- d figure which can be folded to form a 3- D figure, is known as net.

Eg:- Net of a cube is presenting below:-

Diagram of Net of a Cube of NCERT Chapter Visualising Solid Shapes

(5)Types of sketches of solids-

(i)Oblique sketch-

A sketch which does not have proportional lengths but describes all parts of the solid is knows as oblique sketch.

Eg:- Oblique sketch of cube

 

Oblique Sketch of NCERT Chapter Visualising Solid Shapes

(ii) Isometric sketch –

A sketch which have proportional lengths and describes all parts of the solid is knows as an isometric sketch. It is drawn on an isometric dot paper.

Eg:- Isometric sketch of cube

 

Isometric Sketch of NCERT Chapter Visualising Solid Shapes

(6) Different sections of a solid can be viewed in many ways-

(i) Cross- section-

When a solid is viewed by its slice or cutting is known as cross- section of that solid shape.

Types of cross-section

(a) Horizontal cut-

When a solid is cut parallel to its base is known as horizontally cut of that solid shape.

Eg:-Horizontal cut of the vegetables

 

Horizontal Cut of NCERT Chapter Visualising Solid Shapes

                                  Horizontal cut of the papaya

(b)Vertical cut –

When a solid is cut perpendicular to its base is known as vertical cut.

Eg:- Vertical cut of vegetables

 

Vertical Cut of NCERT Chapter Visualising Solid Shapes

             Vertical cut of the papaya

(ii) Shadow play-

When a solid (3-D) is viewed by its 2-D shadow is known as shadow play of that solid shape.

Eg:-

Shadow of people

 

Shadow of NCERT Chapter Visualising Solid Shapes

 

(iii)Certain angle play

When a solid shape is viewed from the different angles is known as certain angle play.

(a)Front view-

When an observer is standing in front of the object is known as front view.

 

 

Front View of NCERT Chapter Visualising Solid Shapes

                                         Front view of telephone

 

(b)Back view

When an observer is standing in back of the object is known as back view.

Back View of NCERT Chapter Visualising Solid Shapes

                      Back view of telephone

 

(c)Side view

When an observer is standing by the side of the object is known as side view.

Side View of NCERT Chapter Visualising Solid Shapes

                                Side view of telephone

(d)Top view

When an observer is standing at the top of the object is known as top view.

Top View of NCERT Chapter Visualising Solid Shapes

                                 Top view of telephone

(7) Map-

A map is a pictorial presentation of a definite place.

Eg:- Map of school, map of market, map of city, map of country etc.

(8) Polyhedra-

A 3D shape with flat polygonal faces, straight edges and sharp corners (vertices), is known as polyhedra. Plural of polyhedra is known as polyhedron.

Eg:- Square, cubes, pyramid, prism etc.

(i) Prism-

Prism is a polyhedron whose base and top are congruent polygons and whose lateral faces are parallelogram in shape. A prism is named after its base, as a hexagonal prism has hexagon base.

Prism of NCERT Chapter Visualising Solid Shapes

(ii) Pyramid-

A pyramid is a polyhedron whose base is a polygon of any number of sides and whose lateral faces are triangles with a common vertex. A pyramid is named after its base, as a hexagonal pyramid has hexagon base.

Pyramid of NCERT Chapter Visualising Solid Shapes

(9) Types of polyhedron

(i)Convex polyhedron-

Convex polyhedron are those polyhedron that have no portions of their diagonals in their exteriors.

Eg:-

Convex Polyhedron of NCERT Chapter Visualising Solid Shapes

(ii)Concave polyhedron

Concave polyhedron are those polyhedron that have some portion of their diagonal in the exteriors.

Eg:-

Concave Polyhedron of NCERT Chapter Visualising Solid Shapes

(iii)Regular polyhedron-

The polyhedron that have faces made up of regular polygons and the same number of faces meet at each vertex, are called regular polyhedron.

Eg:-

Regular Polyhedron of NCERT Chapter Visualising Solid Shapes

(iv)Irregular polyhedron.-

The polyhedron that have faces made up of irregular polygons and the same number of faces do not meet at each vertex, are called irregular polyhedron.

Eg:-

Irregular Polyhedron of NCERT Chapter Visualising Solid Shapes

Euler’s Formula is a relationship among faces (F), vertices (V) and edges (E) of polyhedron.

Euler’s Formula

F + V – E = 2

Helping Topics

NCERT solutions,class 7

NCERT Solutions Class 8

 

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