Question

verify euler's formula for a hexagonal prism

Answer 1

Vertices=6
Faces= 6
Edges=8
L.H.S                  R.H.S
V+F                     2+8
6+6                       10
12
L.H.S IS not equal to R.H.S
Hencw,not verified
                                                  Or
V+F+E=2
6+6+8=2
12+8=2
12=8-2
12=6
HENCE NOT VERIFEIED

Answer 2

Euler's formula for hexagonal prism is verified.

Given : The given three dimensional shape is hexagonal prism.

To find : Verification of Euler's formula for the given three dimensional shape.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to verify Euler's formula for the given shape)

Now, the Euler's theorem state that (for a polyhedron) :

Faces + Vertices - Edges = 2

In case of a hexagonal prism :

1. Vertices = 12
2. Edges = 18
3. Faces = 8

By, putting the available data in the LHS of the Euler's formula, we get :

= Faces + Vertices - Edges

= 8 + 12 - 18

= 2

= RHS (proved)

Hence, Euler's formula for hexagonal prism is verified.

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