Final answer:
Euler's law states V - E + F = 2, and for an octagonal pyramid with 9 vertices, 16 edges, and 9 faces, applying Euler's formula confirms that 9 - 16 + 9 equals 2, verifying the law.
Step-by-step explanation:
The student is asking to verify Euler's law for an octagonal pyramid. Euler's formula, which relates the number of vertices (V), edges (E), and faces (F) of a polyhedron, states that V - E + F = 2.
For an octagonal pyramid, which has 9 vertices (one at the top and eight at the base), 16 edges (eight base edges and eight side edges), and 9 faces (one octagonal base and eight triangular faces), the formula can be verified as follows:
- V = 9 vertices
- E = 16 edges
- F = 9 faces
Applying Euler's formula:
V - E + F = 9 - 16 + 9 = 2
Thus, Euler's law is verified for an octagonal pyramid.