Assinale qual das opções abaixo apresenta o número de faces, arestas e vértices, nessa ordem, de um poliedro convexo.
A)19; 37 e 18
B)19; 37 e 20
C)17; 36 e 20
D)19; 35 e 20
E)17; 37 e 20

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Resposta :

SOLKARPEDGO SOLKARPEDGO · Answer 1

✅ Teorema de Euler:

Seja o teorema de Euler:

[tex]\large\displaystyle\text{$\begin{gathered}V - A + F = 2 \end{gathered}$}[/tex]

Testando o teorema de Euler para cada uma das opções: temos:

A)

[tex]\large\displaystyle\text{$\begin{gathered}18 - 37 + 19 \neq 2 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}0 \ne 2 \end{gathered}$}[/tex]

B)

[tex]\large\displaystyle\text{$\begin{gathered}20 - 37 + 19 = 2 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}2 = 2 \end{gathered}$}[/tex]

C)

[tex]\large\displaystyle\text{$\begin{gathered}20 - 36 +17 \neq 2 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}1 \neq 2 \end{gathered}$}[/tex]

D)

[tex]\large\displaystyle\text{$\begin{gathered}20 - 35 + 19 \neq 2 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}4 \ne 2 \end{gathered}$}[/tex]

E)

[tex]\large\displaystyle\text{$\begin{gathered}20 - 37 + 17 \neq 2 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}0 \neq 2 \end{gathered}$}[/tex]

✅ Portanto, a resposta correta é:

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