In the previous section, you investigated cross sections and slices of prisms and cylinders – 3-dimensional figures with 2 congruent, parallel bases. In this section, you will investigate cross sections and slices of pyramids and cones – 3-dimensional figures with only one base.
To begin with, let’s investigate pyramids. Click on the link Interactive Cross Section Flyer. When the sketch opens, scroll down to the control bars and boxes beneath the 3-dimensional figure and the graph.
Pyramid | Shape of Cross-Section |
Triangular |
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Rectangular |
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Pentagonal |
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Hexagonal |
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Heptagonal |
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Octagonal |
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What relationship do you notice between the shape of the base of a pyramid and the shape of the cross-section? (Reminder: a cross-section is parallel to the base of a pyramid). Why do you think that relationship is true?
Shape of Slice |
Intersection with Base and Lateral Faces |
What patterns and relationships do you observe between the possible shapes of slices of pyramids when the angle of intersection is not parallel to the base of the pyramid?
What is the minimum number of sides in the polygon created by slicing a pyramid at any angle? What is the maximum number of sides?
What relationships do you notice between the total number of faces in the pyramid and the number of sides in the polygons created by slicing the pyramid at angles that are not parallel to the base? Why do you think this is the case?