Question

Using Euler's formula find the missing numbers in the table:

$\begin{array}{cccc}Faces& ?& 5& 20\\ Vertices& 6& ?& 12\\ Edges& 12& 9& ?\end{array}$ [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,

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

In second column,

$5+V-9=2,\Rightarrow V=6$

In third column,

$20+12-?=2,\Rightarrow E=30$

$\begin{array}{cccc}Faces& 8& 5& 20\\ Vertices& 6& 6& 12\\ Edges& 12& 9& 30\end{array}$