Unit 5, Lesson 2
Slicing Solids
Geometry
2.1
Warm-up
Imagine slicing a cylinder with a straight cut. The flat surface you sliced along is called a cross‑section. Try to sketch all the possible kinds of cross-sections of a cylinder.
2.2
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Your teacher will give your group a three-dimensional solid to analyze.
Each question shows several parallel cross-sectional slabs of the same three-dimensional solid. Name each solid.
Here are some three-dimensional solids that may be familiar:
A cross-section is the intersection of a solid with a plane, which is a two-dimensional figure that extends forever in all directions. For example, some cheese is sold in cylindrical blocks. If the cheese is placed on one end and sliced vertically, the slice will reveal a rectangle, as shown. This rectangle is a cross-section of the cylinder.
Here are 3 more examples of cross-sections created by intersecting a plane and a cylinder.
These pieces of cheese are thin cylinders. They are like cross-sections, but they are three-dimensional. All the cuts were made parallel to one another. By looking at the slices, or by stacking them up, we can figure out that the original shape of the cheese was a cylinder.
What if another cheese plate contained slices whose radii got bigger to a maximum size and then got smaller again? The cheese was probably in the shape of a sphere. A sphere has circular cross-sections. The size of the circular cross-sections increases as they get closer to the center of the sphere, and then decreases past the center.
A cross-section is the two-dimensional figure formed by intersecting a solid with a plane.
These diagrams show that the shape of the cross-section depends on how the plane intersects the solid.