A day full of math games & activities. Find one near you.

Which of the following cannot be true for a polyhedron?
(a) V = 4, F = 4, E = 6
(b) V = 6, F = 8, E = 12
(c) V = 20, F = 12, E = 30
(d) V = 4, F = 6, E = 6

Solution:

We have to find the condition which cannot be true for a polyhedron.

Euler’s formula for any polyhedron is, F + V – E = 2

Where F stands for number of faces,

V for number of vertices

E for number of edges.

Considering V = 4, F = 4, E = 6

F + V - E = 4 + 4 - 6

= 8 - 6

= 2

Therefore, V = 4, F = 4, E = 6 can be true for a polyhedron.

Considering V = 6, F = 8, E = 12

F + V - E = 8 + 6 - 12

= 14 - 12

= 2

Therefore, V = 6, F = 8, E = 12 can be true for a polyhedron.

Considering V = 20, F = 12, E = 30

F + V - E = 12 + 20 - 30

= 32 - 30

= 2

Therefore, V = 20, F = 12, E = 30 can be true for a polyhedron.

Considering V = 4, F = 6, E = 6

F + V - E = 6 + 4 - 6

= 10 - 6

= 4

Therefore, V = 4, F = 6, E = 6 cannot be true for a polyhedron.

✦ Try This: Which of the following can be true for a polyhedron?

(a) V = 14, F = 4, E = 6

(b) V = 6, F = 8, E = 12

(c) V = 20, F = 22, E = 30

(d) V = 6, F = 6, E = 10

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

NCERT Exemplar Class 8 Maths Chapter 6 Problem 17

Summary:

V = 4, F = 6, E = 6 cannot be true for a polyhedron

☛ Related Questions: