**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.

** 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 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 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:-**

A cube has 12 edges.

**(iii) Faces-**

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

**Eg:-**

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:-

**(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

**(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.

**Eg:-**

Shadow of people

**(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 telephone**

**(b)Back view **

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

** 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 telephone**

**(d)Top view **

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

** 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.

**(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.

**(9) Types of polyhedron**

**(i)Convex polyhedron-**

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

**Eg:-**

**(ii)Concave polyhedron**

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

**Eg:-**

**(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:-**

**(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:-**

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**