Question

Determine if the shape is a polyhedron using Eulers formula choices: 8, 12, 3, 5,9, 2, 18

Answer 1

Given:

The given shape is a polyhedron.

Required:

We need to use Euler's formula for the given shape.

Step-by-step explanation:

Consider Euler's formula.

`V-E+F=2`

where V is the number of vertices, E is the number of edges and F is the number of faces.

Recall that a vertex is a corner.

The number of corners in the given shape is 12.

`V=12`

Recall that an edge is a line segment between faces and a face is a single flat surface.

The number of edges in the given shape is 18.

`E=18`

The number of faces in the given shape is 8.

`F=8`
`V-E+F=12-18+8`
`V-E+F=2`

The given shape satisfied Euler's formula.

So it is a polyhedron.

Final answer:

`V=12`
`E=18`
`F=8`
`V-E+F=2`

The given shape is a polyhedron.