Definition
Cross-section
A cross-section is the flat shape made where a plane slices through a three-dimensional solid.
What it means
Picture cutting straight through a solid and looking at the fresh flat cut. The flat shape of that cut is the cross-section. Move or turn the cutting plane, and the cross-section can change even though the solid stays the same.
Remember it
Slice, look at the cut, see a flat shape.
Example
Slice an upright circular cylinder straight across, parallel to its circular bases. The cross-section is a circle. Slice the same cylinder vertically through its centre, and the cross-section is a rectangle. The solid stayed the same; the direction of the slice changed.
Watch for
The outside surface seen before cutting is not a cross-section. The cross-section is only the 2-D shape where the cutting plane meets the solid.
Common mix-up
A cross-section is not always the same shape as the solid’s base. A differently directed slice can make a different shape.
Exact meaning
A cross-section is the two-dimensional figure formed by the intersection of a three-dimensional solid and a cutting plane. Its shape and size depend on the solid and on the plane’s position and direction.