Practice and Problem-Solving Exercises

A Practice

See Problem 1.

For each polyhedron, how many vertices, edges, and faces are there? List them.

See Problem 2.

For each polyhedron, use Euler's Formula to find the missing number.

9. faces: □ white square

   edges: 15

   vertices: 9

10. faces: 8

    edges: □ white square

    vertices: 6

11. faces: 20

    edges: 30

    vertices: □ white square

Use Euler's Formula to find the number of vertices in each polyhedron.

12. 6 square faces
13. 5 faces: 1 rectangle and 4 triangles
14. 9 faces: 1 octagon and 8 triangles

See Problem 3.

Verify Euler's Formula for each polyhedron. Then draw a net for the figure and verify Euler's Formula for the two-dimensional figure.

See Problem 4.

Describe each cross section.

See Problem 5.

Visualization Draw and describe a cross section formed by a vertical plane intersecting the cube as follows.

21. The vertical plane intersects the front and left faces of the cube.
22. The vertical plane intersects opposite faces of the cube.
23. The vertical plane contains the red edges of the cube.

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