NCERT Solutions for Class 8 Maths Chapter 10 Exercise 10.3

NCERT Solutions for Class 8 Maths Chapter 10 Exercise 10.3 (Ex. 10.3) Visualising Solid Shapes in PDF file format free to use online as well as offline for CBSE session 2021-2022.

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Class 8 Maths Chapter 10 Exercise 10.3 Solution

Class: 8Mathematics
Chapter: 10Visualising Solid Shapes
Exercise: 10.3Free Solution and Explanation

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Class 8 Maths Chapter 10 Exercise 10.3 Solution in Videos

Class 8 Maths Chapter 10 Exercise 10.3 Solution
Class 8 Maths Chapter 10 Exercise 10.3 Explanation

Euler’s Relation for 3-Dimensional Figures

In a 3-dimnsional figure, let the number of faces be F; the number of edges be E and the number or vertices be V.
Then, the Euler’s relation is given by
F – E + V = 2.

Verification of Euler’s Relation for Various Figures:
1. A Cube or A Cuboid:

Number of faces = 6
Number of edges = 12
Number of vertices = 8
F = 5, E = 9 and V= 8
So, (F – E + V) = (6 – 12 + 8) =2

2. Prism:
I. Triangular Prism:

Number of faces = 2, triangular + 3 rectangular = 5
Number of edges = 9
Number of vertices = 6
So, F = 5, E = 9 and V= 6 (F – E + V) = (5 – 9 + 6) = 2

II. Square prism:

Number of faces = 2 squares + 4 rectangles = 6
Number of edges = 12.
Number of vertices = 8.
So, F = 6, E = 12 and V= 8 (F – E + V) = (6 – 12 + 8) = 2



III. Pentagonal Prism:

Number of faces = 2 pentagons + 5 rectangles = 7
Number of edges = 15
Number of vertices = 10.
So, F = 7, E = 15 and V= 10 (F – E + V) = (7- 15 + 10) = 2

IV. A right prism having each of the bases a polygon of n-sides:

Number of faces = 2 polygons of n sides + n rectangles = (n + 2)
Number of edges = 3n
Number of vertices = 2n
So, F = (n + 2), E = 3 and V= 2n (F – E + V) = (n + 2 – 3n + 2n) = 2

3. Pyramids:
I. Triangular pyramid (Tetrahedron):

Number of faces = 4
Number of edges = 6
Number of vertices = 4
So, F =4, E = 6 and V= 4 (F – E + V) = (4 -6 + 4) =2

II. Square Pyramid:

Number of faces = 1 squares + 4 rectangles = 5
Number of edges = 8
Number of vertices = 5
So, F = 5, E = 8 and V= 5 (F – E + V) = (5 – 8 + 5) = 2

III. Pentagonal Pyramid:

Number of faces = 1 pentagons + 5 rectangles = 6
Number of edges = 10
Number of vertices = 6
So, F = 6, E = 10 and V= 6 (F – E + V) = (6 – 10 + 6) = 2

IV. A Pyramid whose base is a polygon of n-sides:

Number of faces =1 polygons of n sides + n rectangles = (n +1).
Number of edges = 2n
Number of vertices = (n + 1)
F = (n + 1), E =2n and V= (n + 1) (F – E + V) = (n + 1) – (2n) + (n + 1)] = 2

What is the difference between a rectangular prism and a cuboid?

A cuboid has a square cross-sectional area and a length, that is possibly different from the side of the cross-section. It has 8 vertices, 12 sides, 6 faces. A rectangular prism has a rectangular cross-section. It may not stand vertical, if you make it stand on the cross sectional base.

What is the meaning of Euler’s formula?

Euler’s formula, Either of two important mathematical theorems of Leonhard Euler. It is written F + V = E + 2, where F is the number of faces, V the number of vertices, and E the number of edges. A cube, for example, has 6 faces, 8 vertices, and 12 edges, and satisfies this formula.

What is Euler’s rule used for?

Euler’s formula relates the complex exponential to the cosine and sine functions. This formula is the most important tool in AC analysis. It is why electrical engineers need to understand complex numbers.

What is the relationship between the number of faces vertices and edges?

The theorem states a relation of the number of faces, vertices, and edges of any polyhedron. The Euler’s formula can be written as F + V = E + 2, where F is the equal to the number of faces, V is equal to the number of vertices, and E is equal to the number of edges.

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