## Introduction

Visualising Solid Shapes Class 8 Notes provided here are the right tool for students to study productively and score better marks in the exams. Chapter 10 notes will help students get a complete overview of the chapter and also a clear insight into the important topics to remember. The CBSE notes further come with detailed information about each topic and students can have an effective revision before the exams.

### Two Dimensional Object

A shape with only **two dimensions** (such as length and width) and no thickness is calledÂ two-dimensional shape.Â Squares, Circles, Triangles, etc areÂ two dimensional objects. Also known as** “2D”.**

### Area

**Area** is measurement of space enclosed by a closed geometrical figure.

### Volume

**Volume** isÂ measurement ofÂ total space occupied by a solid.

### Three Dimensional Objects- Solids

Shapes which can be measured in 3 directions are called **three-dimensional shapes**. These shapes are also called **solid shapes**. Length, width, and height (or depth or thickness) are their dimensions.

### Formation of Solid Solids

Stacking of 2 dimensional figures, results in solids shapes.

Example: Linear stacking of circles, forms the solid shape called cylinder.

## Solids and Their Classification

### Hexagon

In geometry, **hexagon **is a **polygon with 6 sides**. Sum of all interior angles is equal to 720Â°.

If all the sides of hexagon are equal then it is called regular hexagon, then each interior angle measures 120Â°.

### Non-Polyhedrons

Solids with** curved faces** are called **Non polyhedrons. **They also can be discribed as solids whichÂ have sides that are not polygons.

Example: Sphere, Cylinder, Cone, etc.

### Polyhedrons

A **Polyhedron** is a **solid** in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices. In short,Â **Solids** with flat surfaces are called **Polyhedrons**.**(or** **Polyhedra)**

**Regular polyhedron**: All faces constitute regular polygons and at each vertex the same number of faces intersect. Example : Cube

### Solid Cuboid

A **cuboid** is a solid bounded by six rectangular plane regions.

It is formed by stacking rectangles linearly.

### Solid Triangular Prism

**Solid Triangular Prism**: A **polyhedron** with **two triangularÂ bases parallel to each other**. It is formed by stacking triangles linearly.

### Solid Hexagonal Prism

**Solid Hexagonal Prism**: A polyhedron with two **hexagonalÂ bases parallel to each other.** It is formed by stacking hexagons linearly. Each face of hexagonal prism is rectangular in shape.

### Solid Cylinder

**Solid cylinder**Â can be formed in two different ways:

(i) By stacking rectangles in a circular fashion.

(ii) By stacking many circles linearly

### Solid Sphere

**Solid spheres** are formed by stacking circles in a circular fashion.

### Solid Cone

**Solid Cones**Â are formed by stacking triangles which are right-angled, in a circular fashion with edge which is right angled at the center.

### Formation of Hollow Solids

**Hollow Solids** are obtained by joining two dimensional figures.

### Hollow Cuboid

**Hollow Cuboid**: Formed by joining six rectangles in a specific manner as shown below:

### Hollow Triangular Prism

**Hollow triangular prism**: Formed by joining two triangles and three rectangles in a specific manner as shown below:

### Hollow Hexagonal Prism

**Hollow hexagonal Prism**: Formed by joining two hexagons and six rectangles as shown below:

**Hollow Hexagonal Prism**

### Hollow Cylinder

**Hollow Cylinder**: A cylinder isÂ madeÂ by rotating aÂ rectangleÂ around either its length or breadth as shown below.

### Hollow Cone

**Hollow Cone**: A circle and a curved sector of a circle are joined together as shown below:

**Hollow Cone**

### Pyramid

**Pyramid**: All side faces are triangular in shape and base is of the shape of any polygon.

### Types of Polyhedrons

**Polyhedrons** are of two types:

**(i)** **Convex Polyhedron**:

A polyhedron whose surface (comprising its faces, edges and vertices) does not intersect itself.

Line segment joining any two points of the polyhedron lies within its interior part or on surface.

**(ii) Concave Polyhedron:**

A polyhedron whose surface intersect itself.

Line segment joining any two points of the polyhedron may lie in the exterior part.

### Faces, Edges and Vertices

Every individual **flat surface** of a** solid **is called its **face**. Solids have more than one face.

**Example**: Cube and cuboids have six faces.

**Line segment** which acts as an interface between **two faces** is called an **edge**. It is the line segment that joins two vertices.

Example: Cube and cuboids have 12 edges.

A **vertex **is a point where** two or more edges meet**. These areÂ corner points.

Example: Cube and cuboids have 8 vertices.

### Euler’s Formula

Euler’s Formula:Â For any** polyhedron,**

F+Vâˆ’E=2,

where â€˜Fâ€™ stands for number of **faces,**Â V stands for number of **vertices** and E stands for number of **edges**.

## Perspectives of 3D Shapes

### Perspectives of Looking at a Solid

Side, front and top view of the above solid (made up of cubes) is as shown below:

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