Can a polyhedron have V = F = 9 and E = 16 ? If yes, draw its figure.

Solution:

Given, V = F = 9

E = 16

We have to determine if the given values satisfy Euler’s formula.

Euler’s formula for any polyhedron is given by

F + V – E = 2

Where F stands for number of faces,

V for number of vertices

E for number of edges.

Now, F + V - E = 9 + 9 - 16

= 18 - 16

= 2

Therefore, the given values satisfy Euler’s formula.

An octagonal pyramid has 9 vertices, 9 faces, and 16 edges.

Therefore, the given values form an octagonal pyramid.

✦ Try This: Can a polyhedron have V = F = 10 and E = 18 ? If yes, draw its figure.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 10

NCERT Exemplar Class 8 Maths Chapter 6 Problem 71

Can a polyhedron have V = F = 9 and E = 16 ? If yes, draw its figure.

Summary:

A polyhedron can have V = F = 9 and E = 16. The figure is mentioned above.

☛ Related Questions:

• Check whether a polyhedron can have V = 12, E = 6 and F = 8
• A polyhedron has 60 edges and 40 vertices. Find the number of its faces
• Find the number of faces in the given shapes