 # Visualising Solid Shapes Class 8 Notes: Chapter 10

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.

Some of the key concepts discussed in the notes include;

• Introduction
• Views of 3D-Shapes
• Mapping Space
• Faces, Edges and Vertices
• Related Terms
• Euler’s formula
• Important Questions

## Introduction

Students already learn about shapes in class 7. However, they will deal with the topic in greater detail in class 8. Let’s understand some of the topics below.

Plane shapes or 2-D shapes

Any shape that can be drawn on a plane is called a plane figure. The plane figures are 2-D shapes, as they have two dimensions, i.e., length and breadth. Examples include circle, square, and triangle. Solid shapes or 3-D shapes

Any shape that occupies space is called a 3-D shape. These shapes have three dimensions, i.e., height, length, and breadth. Most of the time 3-D shapes look different from different positions, which are, front view, side view and top view. Examples include cylinder, sphere, cube, cuboid, and cone. ### Views of 3D-Shapes

Generally, when a talk about 3-D objects, when they are viewed from different positions they tend to appear a bit different. ### Mapping Space

A map is quite different from a picture of a place. A map shows the location of a place or an object with respect to other objects or places. In a map, students should be aware of;

• Different objects, places, etc. are represented by symbols.
• Size of objects remains proportional to their actual size irrespective of the distance from the observer.
• All the lengths are drawn in reference to an assigned scale.

### Faces, Edges and Vertices

• Face: Refers to plane figures which make up solids.
• Edge: Line segments where faces meet.
• Vertices/Vertex: Points where edges meet. Related Terms:-

1. Polyhedrons: Solids which come with faces, edges and vertices are known as polyhedrons.
2. Non – Polyhedrons: Solids which do not contain either edges, faces, or vertices are categorized as non-polyhedrons.
3. Convex Polyhedron: It is a polyhedron in which the line segment formed on joining any vertices is found completely inside it.
4. Concave Polyhedron: Here the vertices lie on the outside.
5. Regular Polyhedron: A polyhedron having the same number of faces as vertices.
6. Prism: A polyhedron which has its base and top as the congruent polygons. Its sides are made of parallelograms.
7. Pyramid: A polyhedron having polygon as its base and the lateral faces are triangles with a common vertex.

### Euler’s formula

 F + V – E = 2 or F + V = E + 2
• F stands for the number of faces
• E stands for the number of edges
• V stands for the number of vertices

### Important Questions

1. How many faces does a polyhedron have?

i. 2 triangles ii. 3 triangles iii. 4 triangles and a square

1. Does square prism bear similarity to a cube. Explain
2. Find the missing numbers using Euler’s formula:
 Faces 5 20 Vertices 6 12 Edges 12 9