Question

Verify Euler's formula for a pentagonal pyramid

Answer 1

Euler's formula-
F-E+V=2
6-10+6=2
12-10=2
2=2
verified
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Answer 2

Euler's formula for a pentagonal pyramid is verified

Given :

Pentagonal pyramid

To find :

To verify Euler's formula for a pentagonal pyramid

Concept :

Euler’s formula for Polyhedron :

For polyhedron F + V = E + 2

Where F stands for number of faces , V stands for number of vertices , E stands for number of edges .

Solution :

Step 1 of 2 :

Write down number of faces , number of vertices , number of edges

For pentagonal pyramid :

F = Number of faces = 7

V = Number of vertices = 10

E = Number of edges = 15

Step 2 of 2 :

Verify Euler's formula for a pentagonal pyramid

By Euler’s formula F + V = E + 2

LHS = F + V = 7 + 10 = 18

RHS = E + 2 = 15 + 2 = 17

Thus LHS = RHS

Hence Euler's formula for a pentagonal pyramid Verified

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