Class 8 Maths Chapter 10 Notes - Visualising Solid Shapes

Views of 3 D Shapes

Shapes that have length, width, as well as thickness (or height) are called three-dimensional shapes. These shapes are also called solid shapes. The majority of objects present in our physical world are three-dimensional. When we look at a 3-D object from different positions, we find differences in its top view, front view and side view.

Let's define them one-by-one.

Top View: When we look at a shape exactly from the top, the view obtained is the top view of the shape.

Front View: When we look at a shape from the front, the view obtained is the front view of the shape.

Side View: When we look at a shape from any of its side, the view obtained is the side view of the shape.

Let’s see an example based on the view of a 3-D object.

A block and its three views are shown in the image. Identify the top view.



The image shown as option (b) is the top view of the block.

Maps

We often use a map to visit our favourite eating place, shop, picnic point, etc. Apart from the maps on our phones, we see maps on a piece of paper or big charts, as shown in the image on the left. There are different symbols and signs on it which help us to understand the location, route, turns, etc.

A map shows everything in proportion to its actual size. It means that the size of the objects with respect to each other will remain the same, irrespective of how the observer looks at them. We use a particular scale to draw a map so that the lengths drawn are proportional to the size of the original figures.

Polyhedrons

The faces of 3-D objects resemble with polygons. For example, if we hold a matchstick box, we see that its top face resembles a rectangle, which is a polygon. A polygon is a geometrical shape with several vertices and a number of edges joining each other.

Rectangle has sides and vertices. Since, this rectangle is a part of that matchstick box, we can say that the matchstick box also has edges and vertices. Such 3-D objects, made by joining several polygons together are known as polyhedrons.

Parts of Polyhedrons

Face: The flat surface of a 3-D shape is called its face.

Edge: Edge is the line where the two surfaces (faces) meet. These lines make the structure of the solid shapes.

Vertex: The edges meet each other at a point, we call these points as vertices. Vertices are the corners of a solid shape.

Now we'll learn about the different types of polyhedrons.

NCERT Solutions for Class 8 Maths Chapter 10
NCERT Solutions Class 8 Maths Exercise 10.1
NCERT Solutions Class 8 Maths Exercise 10.2
NCERT Solutions Class 8 Maths Exercise 10.3

Types of Polyhedrons

Based on Types of Faces

Regular Polyhedron: A regular polyhedron is made up of faces which are regular polygons. All the sides of this solid are equal. Such solids are also known as ‘platonic solids’. Interestingly, there are only five regular polyhedrons.

● Regular tetrahedron: A 4-faced polyhedron and all the faces are equilateral triangles.
● Cube: A 6-faced polyhedron and all the faces are squares.
● Regular octahedron: An 8-faced polyhedron and all the faces are equilateral triangles.
● Regular dodecahedron: A 12-faced polyhedron and all the faces are regular pentagons.
● Regular icosahedron: A 20-faced polyhedron and all the faces are equilateral triangles.

Irregular Polyhedron: An irregular polyhedron is made up of polygons of different shapes. This means that the sides of an irregular polyhedron are not equal. A prism is an example of an irregular polyhedron.

Based on Number of Facesh

We can also classify polyhedrons on the basis of the number of faces joining together to form the solid object. It is quite easy to name such solids as it starts with the prefix meaning the particular number. Some examples are:

● Pentahedron- A polyhedron with 5 faces.
● Heptahedron- A polyhedron with 7 faces.
● Nonahedron- A polyhedron with 9 faces.
● Decahedron- A polyhedron with 10 faces.

Based on Presence of Diagonals

We can also classify polyhedrons based on the line segment (diagonal) joining any two non-adjacent vertices.

Convex Polyhedron: If all the diagonals of a polyhedron lies inside or on the figure, it is called a convex polyhedron.

Non-Convex or Concave Polyhedron: If one or more diagonal of the polyhedron lies outside the figure, it is called a non-convex polyhedron.

Let us study about prisms and pyramid.

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Prism & Pyramid

There are two special type of polyhedrons.

Prism

A prism is a polyhedron, having two of its bases parallel and the side faces are parallelograms. The top and bottom faces of the prism are polygons parallel to each other.

Pyramid

A pyramid is a polyhedron where the base is a polygon and the side faces are triangles with a common vertex at the top.

Euler’s Formula

If we know the number of faces and the number of vertices of a polyhedron, we can find out the number of edges using the ‘polyhedron formula’ or Euler’s formula.

F + V = E + 2 or F + V – E = 2

where, F is the number of faces of the polyhedron,
V is the number of vertices of the polyhedron,
E is the number of edges of the polyhedron.

Example

Find the number of faces for a polyhedron with 5 vertices and 9 edges.

Using, F + V = E + 2 and putting the values,
F + 5 = 9 + 2
F = 11 – 5
F = 6

Hence, the number of faces is 6.

Links to Other Resources for Class 8 Maths

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