Complete the table by using Euler's formula.
$F$ $8$ $5$ ?
$V$ $6$ ? $12$
$E$ ? $9$ $30$

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Solution

Euler's Formula $V + F - E = 2$
i)
$F = 8, V = 6$
$6 + 8 - E = 2 ⟹ E = 12$
ii)
$F = 5, E = 9$
$V + 5 - 9 = 2 ⟹ V = 6$
iii)
$V = 12, E = 30$
$12 + F - 30 = 2 ⟹ F = 20$

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

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Complete the table by using Euler's formula.F85?V6?12E?930

Euler's Formula V+F−E=2i)F=8,V=66+8−E=2⟹E=12ii)F=5,E=9V+5−9=2⟹V=6iii)V=12,E=30 12+F−30=2⟹F=20

Complete the table by using Euler's formula.
$F$ $8$ $5$ ?
$V$ $6$ ? $12$
$E$ ? $9$ $30$

Euler's Formula $V + F - E = 2$
i)
$F = 8, V = 6$
$6 + 8 - E = 2 ⟹ E = 12$
ii)
$F = 5, E = 9$
$V + 5 - 9 = 2 ⟹ V = 6$
iii)
$V = 12, E = 30$
$12 + F - 30 = 2 ⟹ F = 20$