Using Euler's formula find the value of unknown x and y. faces = 7, y . vertices = 10,12. edges = x, 18
Answers
Explanation:
Using Euler's formula find the value of unknown x and y. faces = 7, y . vertices = 10,12. edges = x, 18. I have also same doubt bro
Answer:
As per question:
Euler's Formula is for any polyhedrons. i. e.
F + V - E = 2
Where, F = Faces and V = Vertices and E = Edges
i) Given, F = 7 and V = 10 and E = x
According to the formula:
7 + 10 - x = 2
17 - x = 2
-x = 2 - 17
x = 15
ii) Given, F = y and V = 12 and E = 18
According to the formula:
12 + y - 18 = 2
-6 + y = 2
y = 2 + 6
y = 8
iii) Given, F = 9 and V = z and E = 16
According to the formula:
9 + z - 16 = 2
-7 + z = 2
z = 2 + 7
z = 9
iv) Given, F = p and V = 6 and E = 12
According to the formula:
p + 6 - 12 = 2
p - 6 = 2
p = 2 + 6
p = 8
v) Given, F = 6 and V = q and E = 12
According to the formula:
6 + q - 12 = 2
-6 + q = 2
q= 2 + 6
q = 8
vi) Given, F = 8 and V = 11 and E = r
According to the formula:
8 + 11 - r = 2
19 - r = 2
r = 19 - 2
r = 17
As per question:
Euler's Formula is for any polyhedrons. i. e.
F + V - E = 2
Where, F = Faces and V = Vertices and E = Edges
i) Given, F = 7 and V = 10 and E = x
According to the formula:
7 + 10 - x = 2
17 - x = 2
-x = 2 - 17
x = 15
ii) Given, F = y and V = 12 and E = 18
According to the formula:
12 + y - 18 = 2
-6 + y = 2
y = 2 + 6
y = 8
iii) Given, F = 9 and V = z and E = 16
According to the formula:
9 + z - 16 = 2
-7 + z = 2
z = 2 + 7
z = 9
iv) Given, F = p and V = 6 and E = 12
According to the formula:
p + 6 - 12 = 2
p - 6 = 2
p = 2 + 6
p = 8
v) Given, F = 6 and V = q and E = 12
According to the formula:
6 + q - 12 = 2
-6 + q = 2
q= 2 + 6
q = 8
vi) Given, F = 8 and V = 11 and E = r
According to the formula:
8 + 11 - r = 2
19 - r = 2
r = 19 - 2
r = 17