Question

Verify Euler's formula for the following solids:
Please mark faces,edges,vertices​

Answer 1

Answer:

Euler's Formula for Polyhedron: ... 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.

Answer 2

Given:

First step we have to find the number of faces, vertices and edges from the given diagram.

To prove:

Euler's formula, F+V-E=2

Solution:

a) From the first diagram

Number of faces(F)=6

Number of vertices (V)=6

Number of Edges (E)=10

Then F+V-E=6+6-10

Then F+V-E=6+6-10 =2

Hence the Euler's formula verified for (a).

b) From the second diagram

Number of faces=8

Number of vertices=12

Number of Edges=18

Then F+V-E=8+12-18

Then F+V-E=8+12-18 =2

Thus the Euler's formula verified for (b).

c) From the third diagram

Number of faces=5

Number of vertices=7

Number of Edges=10

Then F+V-E=5+7-10

Then F+V-E=5+7-10 =2

That fore the Euler's formula verified for (c).