B Apply

24. 1. Open-Ended Sketch a polyhedron whose faces are all rectangles. Label the lengths of its edges.
    2. Use graph paper to draw two different nets for the polyhedron.

25. For the figure shown below, sketch each of following.

    

    1. a horizontal cross section
    2. a vertical cross section that contains the vertical line of symmetry
26. Reasoning Can you find a cross section of a cube that forms a triangle? Explain.
27. Reasoning Suppose the number of faces in a certain polyhedron is equal to the number of vertices. Can the polyhedron have nine edges? Explain.

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

28. The plane is tilted and intersects the left and right faces of the cube.
29. The plane contains the red edges of the cube.
30. The plane cuts off a corner of the cube.

Visualization A plane region that revolves completely about a line sweeps out a solid of revolution. Use the sample to help you describe the solid of revolution you get by revolving each region about line l.

Sample: Revolve the rectangular region about the line l. You get a cylinder as the solid of revolution.

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34. Think About a Plan Some balls are made from panels that suggest polygons. A soccer ball suggests a polyhedron with 20 regular hexagons and 12 regular pentagons. How many vertices does this polyhedron have?

    

    • How can you determine the number of edges in a solid if you know the types of polygons that form the faces?
    • What relationship can you use to find the number of vertices?

Euler's Formula F + V = E + 1 f plus v , equals e plus 1 applies to any two-dimensional network where F is the number of regions formed by V vertices linked by E edges (or paths). Verify Euler's Formula for each network shown.

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