   Chapter 9.CR, Problem 28CR Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

For each of the following solids, verify Euler's equation by determining V , the number of vertices; E , the number of edges; and F , the number of faces.a) Right octagonal prismb) Tetrahedronc) Regular octahedron

To determine

(a)

To verify:

The Euler's equation by determining V, the number of vertices; E, the number of edges; and F, the number of faces for the following solid.

Explanation

Definition:

The number of vertices V, the number of edges E, and the number of faces F of a polyhedron are related by the equation

V+F=E+2

Given:

For the following solid, verify Euler's equation by determining V, the number of vertices; E, the number of edges; and F, the number of faces.

Right octagonal prism

Calculation:

Let us consider the right octagonal prism of the figure.

To determine

(b)

To verify:

The Euler's equation by determining V, the number of vertices; E, the number of edges; and F, the number of faces for the following solid.

To determine

(c)

To verify:

The Euler's equation by determining V, the number of verticals; E, the number of edges; and F, the number of faces for the following solid.

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