Answered

IDNLearn.com is your go-to resource for finding expert answers and community support. Join our Q&A platform to get accurate and thorough answers to all your pressing questions.

Using Euler's formula, how many edges does a polyhedron with 6 faces and 8 vertices have?

Euler's Formula: [tex] F + V = E + 2 [/tex]

[tex] F = 6 [/tex]
[tex] V = 8 [/tex]
[tex] E = ? [/tex]

How many edges does the polyhedron have?

[tex] \text{Edges:} \, E = ? [/tex]

Sagot :

GinnyAnsweridn
To determine the number of edges a polyhedron has using Euler's formula, we follow these steps:

1. Identify the known values:
- Number of faces, [tex]\( F = 6 \)[/tex]
- Number of vertices, [tex]\( V = 8 \)[/tex]

2. State Euler’s formula:
[tex]\[ F + V = E + 2 \][/tex]
This formula relates the number of faces ([tex]\( F \)[/tex]), vertices ([tex]\( V \)[/tex]), and edges ([tex]\( E \)[/tex]) of a polyhedron.

3. Substitute the known values into Euler’s formula:
[tex]\[ 6 + 8 = E + 2 \][/tex]

4. Solve for [tex]\( E \)[/tex] (the number of edges):
[tex]\[ 14 = E + 2 \][/tex]

5. Isolate [tex]\( E \)[/tex] by subtracting 2 from both sides of the equation:
[tex]\[ 14 - 2 = E \][/tex]

6. Simplify the equation:
[tex]\[ E = 12 \][/tex]

Therefore, a polyhedron with 6 faces and 8 vertices has [tex]\( 12 \)[/tex] edges.
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for trusting IDNLearn.com with your questions. Visit us again for clear, concise, and accurate answers.