Cross Sections
Shapes formed when a plane slices a solid.
Key idea
Shapes formed when a plane slices a solid.
In depth
A cross section is the shape you get when a plane slices a solid. Different angles give different shapes: slicing a cone gives a circle, ellipse, parabola or hyperbola.
Worked example
Slicing a cube parallel to a face gives a square; slicing diagonally can give a hexagon.
Real-world uses
- Understanding CT scan slices, cutting a loaf of bread or a rock to see inside it
Common mistake
Assuming the section shape is always the same as the face.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Cross Sections?
Shapes formed when a plane slices a solid. It is a topic at the advanced level in Geometry.
Where is Cross Sections used in real life?
Real-world examples: Understanding CT scan slices, cutting a loaf of bread or a rock to see inside it.
What should I learn before Cross Sections?
Make sure you are comfortable with Nets of Solids, the previous topic in Geometry.
What is a common mistake with Cross Sections?
Assuming the section shape is always the same as the face.
How can I practise Cross Sections?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Cross Sections?
Move on to Cavalieri’s Principle next.
Related advanced topics in Geometry
- Heron’s Formula – Triangle area from three sides.
- Regular Polygon Area – Use apothem and perimeter.
- Arc Length of a Circle – Part of the circumference.
- Sector Area – Part of the circle’s area.
- Central and Inscribed Angles – An inscribed angle is half the central angle on the same arc.
- Chord and Tangent Properties – A tangent is perpendicular to the radius at the point of contact.