NCERT Class 8 Mathematics Solutions: Chapter 10 – Visualising Solid Shapes Exercise 10.3 Part 3

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The values do not satisfy the Euler's formula

The Values Do Not Satisfy the Euler's Formula

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Question 7: Using Euler’s formula, find the unknown:

This table Face vertices and Edges

Faces

?

5

20

Vertices

6

?

12

Edges

12

9

?

Answer:

In first column, F and

Using Euler’s formula, we see

Hence there are 8 faces.

In second column,

Using Euler’s formula, we see

Hence there are 6 vertices.

In third column,

Using Euler’s formula, we see

Hence there are 30 edges.

Question 8: Can a polyhedron have 10 faces, 20 edges and 15 vertices?

Answer:

If .

Then, we know Using Euler’s formula,

L.H.S

R.H.S = 2

.

Therefore, it does not follow Euler’s formula.