Question

Fill the missing numbers in the table:

$\begin{array}{cccc}Faces& ?& 9& 20\\ Vertices& 8& ?& ?\\ Edges& 12& 16& 30\end{array}$ [4 MARKS]

Answer 1

Formula : 1 Mark
Each missing number : 1 Mark each

From Euler’s formula we know that

F + V - E = 2

In first column,

$F+8-12=2\Rightarrow F=6$

In second column,

$9+V-16=2,\Rightarrow V=9$

In third column,

$20+V-30=2,\Rightarrow V=12$

$\begin{array}{cccc}Faces& 6& 9& 20\\ Vertices& 8& 9& 12\\ Edges& 12& 16& 30\end{array}$