Cross Sections – Slicing a Solid to Reveal a 2D Shape
A cross-section is the 2D shape you see when you slice straight through a 3D solid. While a net shows a solid unfolded on the outside, a cross-section reveals what's happening on the inside – and the direction of the cut matters enormously: the same solid can reveal completely different 2D shapes depending on how it's sliced.
This is exactly the idea behind medical imaging like CT and MRI scans, which build up a full 3D picture of the human body from a stack of many 2D cross-sectional “slice” images.
Predicting a Cross-Section
Cutting parallel to a solid's uniform cross-section (like a prism's base, or a cylinder's circular end) reveals a copy of that shape. Cutting a curved solid through its centre often reveals a different shape than cutting parallel to its base.
Slicing straight down through the middle reveals a rectangle, even though the cylinder's ends are circles.
Real-Life Application
- Medical scans: CT and MRI scans build a 3D picture from 2D cross-sectional slices.
- Geology: rock core samples reveal cross-sections of underground layers.
- Cooking: slicing a loaf of bread or a log of cookie dough reveals its cross-section.
Key Takeaways
- A cross-section is the 2D shape revealed by slicing through a 3D solid.
- The direction of the cut determines which 2D shape appears.
- Medical scanning technology relies on this same slicing principle.
Practice: Cross Sections
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