11.1: Prisms, Pyramids, and Polyhedra
Describe each shape as precisely as you can. Click on the applet and drag the mouse to show the object turning in 3D.
Let's see what shapes you get when you slice a three-dimensional object.
Describe each shape as precisely as you can. Click on the applet and drag the mouse to show the object turning in 3D.
Here are a rectangular prism and a pyramid with the same base and same height. Drag the large red point up and down to move the plane through the solids.
If we slice each solid parallel to its base halfway up, what shape cross sections would we get? What is the same about the cross sections? What is different?
If we slice each solid parallel to its base near the top, what shape cross sections would we get? What is the same about the cross sections? What is different?
Describe the cross sections that would result from slicing each solid perpendicular to its base.
Use the applet to draw each cross section and describe it in words.
Here is an applet with a rectangular prism, 4 units by 2 units by 3 units.
When we slice a three-dimensional object, we expose new faces that are two dimensional. The two-dimensional face is a cross section. Many different cross sections are possible when slicing the same three-dimensional object.
Here are two peppers. One is sliced horizontally, and the other is sliced vertically, producing different cross sections.
The imprints of the slices represent the two-dimensional faces created by each slice.
It takes practice imagining what the cross section of a three-dimensional object will be for different slices. It helps to experiment and see for yourself what happens!
A cross section is the two-dimensional figure that is exposed by slicing a three-dimensional object.