Question

Using Euler's formula complete the following table.
[4 MARKS]
$\begin{array}{ccc}\text{Faces}& \text{Vertices}& \text{Edges}\\ 10& 10& ?\\ 8& ?& 18\\ 6& 8& ?\\ ?& 5& 8\\ 12& ?& 19\end{array}$

Answer 1

Formula: 1 Mark
Answers: 3 Marks

Euler's formula: F + V - E = 2

$\Rightarrow$ 1) 10 + 10 - E = 2

E = 20 - 2

E = 18


$\Rightarrow$ 2) 8 + V - 18 = 2

V = 10 + 2

V = 12


$\Rightarrow$ 3) 6 + 8 - E = 2

E = 14 - 2

E = 12


$\Rightarrow$ 4) F + 5 - 8 = 2

F = 2 + 3

F = 5


$\Rightarrow$ 5) 12 + V - 19 = 2

V = 2 + 7

V = 9