To Show: Whether Euler’s formula is true for the given figure.
Answer to Problem 34PPS
The figures expect the figure 6 th do not satisfy the Euler’s formula is not the polyhedron.
Explanation of Solution
Given:
The number of faces
Calculation:
Consider the relation by the Euler’s formula,
Since, the first figure is rectangular prism so there are 8 vertices, 12 edges and the 6 faces that is
Then, replace
This proves the Euler’s formula.
Since, the second figure is square prism so there are 8 vertices, 12 edges and the 6 faces that is
Then, replace
Since, the third figure is triangular prism so there are 6 vertices, 9 edges and the 5 faces that is
Then, replace
Since, the sixth figure is pentagonal pyramid so there are 5 vertices, 8 edges and the 5 faces that is
Then, replace
The sixth figure is the cylinder as that is not the polyhedron.
Thus, the figures expect the figure 6 th do not satisfy the Euler’s formula is not the polyhedron.
Chapter 1 Solutions
Geometry, Student Edition
Additional Math Textbook Solutions
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Elementary Statistics: Picturing the World (7th Edition)
Introductory Statistics (10th Edition)
Linear Algebra and Its Applications (5th Edition)
Introductory Statistics
Trigonometry (11th Edition)
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning