The document discusses Euler's formula, which relates the number of faces (f), vertices (v), and edges (e) of solid figures with the equation f + v = e + 2. It provides examples verifying the formula for a cube, cuboid, triangular prism, and triangular pyramid. Each example confirms that the formula holds true for the given solid figures.

2. EULER'S FORMULA

3.  Euler Formula
 Examples
OUTLINE

4. Leonard Euler, a great Mathematician, at a very young age discovered an
interesting formula regarding the faces, vertices and edges of solid figures.
The Euler Formula is given by, F + V = E + 2
Where F is faces, V is vertices, E is edges of solid figures.
Lets see some examples to verify the above relation
Euler Formula

5. Faces = 6
Edges = 12
Vertices = 8
L.H.S = F + V
= 6 + 8
= 14
R.H.S = E + 2
= 12 + 2
= 14
Thus, the Euler Formula F + V = E + 2 is verified for cube.
Cube :
Similarly, the Euler Formula F + V = E + 2 can be verified for cuboid.
Examples

6. Faces = 5
Edges = 9
Vertices = 6
L.H.S = F + V
= 5 + 6
= 11
R.H.S = E + 2
= 9 + 2
= 11
Thus, the Euler Formula F + V = E + 2 is verified for Triangular Prism.
Triangular Prism :
Examples

7. Faces = 4
Edges = 6
Vertices = 4
L.H.S = F + V
= 4 + 4
= 8
R.H.S = E + 2
= 6 + 2
= 8
Thus, the Euler Formula F + V = E + 2 is verified for Triangular Pyramid.
Triangular Pyramid :
Examples

8.  Today we learnt about :
 Euler Formula
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