Question

For each polyhedron, use Euler's Formula to find the missing number.Face:Edges: 11Vertices: 8Face: 8EdgesVertices: 3FaceEdges: 24Vertices: 16

Answer 1

Given:

(1) Face:

Edges: 11

Vertices: 8

(2) Face: 8

Edges

Vertices: 3

Required:

To find the missing number by using the Euler formula:

Explanation:

The Euler formula is given as:

$V-E+F=2$

Where V = vertices

E = edges

F = faces

Substitute the given values.

(1)

$\begin{gathered} 8-11+F=2 \\ -3+F=2 \\ F=2+3 \\ F=5 \end{gathered}$

(2)

$\begin{gathered} 3-E+8=2 \\ 11-E=2 \\ E=11-2 \\ E=9 \end{gathered}$

(3)

$\begin{gathered} 16-24+F=2 \\ -8+F=2 \\ F=8+2 \\ F=10 \end{gathered}$

Final Answer:

(1) F= 5

(2) E =9

(3) F=10