Use Euler's formula to find the missing number.
Vertices: 23
Edges: 39
Face: ?
Using Euler's formula:
F + V - E = 2
where F is the number of faces, V is the number of vertices, and E is the number of edges.
Plugging in the given values:
F + 23 - 39 = 2
Simplifying:
F - 16 = 2
Adding 16 to both sides:
F = 18
Therefore, the missing number is 18.
Euler's formula states that for a polyhedron, the number of vertices (V), edges (E), and faces (F) are related by the equation: V - E + F = 2.
Given that the number of vertices is 23 (V = 23) and the number of edges is 39 (E = 39), we can substitute these values into the formula and solve for the missing number:
23 - 39 + F = 2
Begin by simplifying the equation:
-16 + F = 2
Next, isolate F by adding 16 to both sides:
F = 2 + 16
Finally, compute the sum:
F = 18
Therefore, the missing number, representing the number of faces, is 18.