VegetaV103784 VegetaV103784
  • 03-11-2022
  • Mathematics
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Using Euler’s formula, how many edges does a polyhedron with 9 faces and 14 vertices have? Thank you

Using Eulers formula how many edges does a polyhedron with 9 faces and 14 vertices have Thank you class=

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SaimF587383 SaimF587383
  • 03-11-2022
[tex]F+V=E+2[/tex]

Solve the Euler's formula above to E (Edges)

[tex]\begin{gathered} \text{Substract 2 in both sides of the equation;} \\ \\ F+V-2=E+2-2 \\ F+V-2=E \\ \\ \text{ Rewrite the equation:} \\ \\ E=F+V-2 \end{gathered}[/tex]

Use the given data;

Faces; F=9

Vertices: V=14

[tex]\begin{gathered} E=9+14-2 \\ E=21 \end{gathered}[/tex]

The polyhedron has 21 edges

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