Using Euler’s formula, find the value of unknown x, y, z, p, q, r, in the following table
Solution:
We have to use Euler’s formula to find the value of unknown x, y, z, p, q, r.
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.
(i) Given, F = 7, V = 10 and E = x
Now, F + V - E = 2
7 + 10 - x = 2
17 - x = 2
x = 17 - 2
x = 15
(ii) Given, F = y, V = 12 and E = 18
Now, F + V - E = 2
y + 12 - 18 = 2
y - 6 = 2
y = 2 + 6
y = 8
(iii) Given, F = 9, V = z and E = 16
Now, F + V - E = 2
9 + z - 16 = 2
z - 7 = 2
z = 2 + 7
z = 9
(iv) Given, F = p, V = 6 and E = 12
Now, F + V - E = 2
p + 6 - 12 = 2
p - 6 = 2
p = 2 + 6
p = 8
(v) Given, F = 6, V = q and E = 12
Now, F + V - E = 2
6 + q - 12 = 2
q - 6 = 2
q = 2 + 6
q = 8
(vi) Given, F = 8, V = 11 and E = r
Now, F + V - E = 2
8 + 11 - r = 2
19 - r = 2
r = 19 - 2
r = 17
Therefore, the values of x, y, z, p, q, r are 15, 18, 9, 8, 8, 17.
✦ Try This: Using Euler’s formula, find the value of unknown x. If, F = V = 9 and E = x
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 10
NCERT Exemplar Class 8 Maths Chapter 6 Problem 70
Using Euler’s formula, find the value of unknown x, y, z, p, q, r, in the following table.
Summary:
Using Euler’s formula, the values of unknown x, y, z, p, q, r are 15, 18, 9, 8, 8, 17.
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