Question

Using Euler's Formula , find number of faces , when E= 20 and V= 15

Answer 1

Given :

• Edges = 20
• Vertices = 15

To Find :

• Faces
• Using Euler's formula.

Euler's Formula :

V - E + F = 2

Vertices + Edges + Face = 2

According to this formula when the values of vertices edges and faces are given of three dimensional object ; the sum of edges and faces subtracted with the vertices must be equal to 2 . This formula can also be used to find the

missing values.

Solution :

V - E + F = 2

15 - 20 + F = 2

-5 + F = 2

Transposing (-5) to the other side of the equal to sign ; changes its sign from (-) to (+) thus making it (5). Following the same ; we get :

F = 2 + 5

F = 7

Verification :

V - E + F = 2

15 - 20 + 7 = 2

-5 + 7 = 2

2 = 2

LHS = RHS

Hence , our answer is verified

Supplementary information :

• Euler's Formula was named its founder , a mathematician called Leonhard Euler.
• Face : The flat area that forms one face of the 3D object.
• Edges : The area where the faces meet.
• Vertices :The place where the edges meet.
• 3D : The object that can be seen , touched and have edges and vertices.