Let's use the applet below to explore cross-sections that are parallel to the base of a prism and pyramid with the same polygon base.
Now let's explore some cross-sections that are perpendicular to the base of a prism and pyramid with the same polygon base.
Recall that prisms have rectangular sides, and the shape on the top and the base is the same. The name of the base shape gives the prism its name.
Any cross-section taken parallel to the base in a prism is always the same shape and size as the base. In other words, we say that a prism has a uniform cross-section.
Recall that pyramids have triangular sides, and the shape of the base gives the prism its name.
In a pyramid, any cross-section taken parallel to the base is always the same shape but is smaller in size than the base.
From the applets, we can see that three-dimensional shapes have more than one cross-section and they may or not be the same shape. It all depends on which way we cut them!
We want to classify the following solid:
Does the shape have a uniform cross-section ?
The solid is a:
Consider the solid in the adjacent figure.
If the solid is cut straight down below the dotted line, what cross-section results?
Does the solid above have a uniform cross-section?
What is the name of the solid?
A triangular prism
A rectangular prism
A hexagonal prism
A pentagonal prism.
Which two of the objects below could have the following cross-section?
Describe the two-dimensional figures (cross sections) that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms, right rectangular pyramids, cones, cylinders, and spheres.