Notes of chapter: Visualising Solid Shapes are presented below. Indepth notes along with worksheets and NCERT Solutions.
(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.
(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.
(3) Parts of 3-D figure-
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.
Vertex is singular form of vertices.
A cube has 8 corners or vertices.
The line segments which join vertices and faces of 3D figures are known as edges.
A cube has 12 edges.
The flat surfaces of 3-D figures are known as faces.
A cube has 6 faces.
In above figure-
ABCD, DCHE, ADEF, BCHG, EFGH and ABFG are faces of a cube.
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:-
(5)Types of sketches of solids-
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
(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
(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 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 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.
Shadow of people
(iii)Certain angle play
When a solid shape is viewed from the different angles is known as certain angle play.
When an observer is standing in front of the object is known as front view.
Front view of telephone
When an observer is standing in back of the object is known as back view.
Back view of telephone
When an observer is standing by the side of the object is known as side view.
Side view of telephone
When an observer is standing at the top of the object is known as top view.
Top view of telephone
A map is a pictorial presentation of a definite place.
Eg:- Map of school, map of market, map of city, map of country etc.
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.
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.
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.
(9) Types of polyhedron
Convex polyhedron are those polyhedron that have no portions of their diagonals in their exteriors.
Concave polyhedron are those polyhedron that have some portion of their diagonal in the exteriors.
The polyhedron that have faces made up of regular polygons and the same number of faces meet at each vertex, are called regular 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.
Euler’s Formula is a relationship among faces (F), vertices (V) and edges (E) of polyhedron.
F + V – E = 2