I use a computer simulation to show you cross-sections of various three-dimensional shapes, when they are cut with a plane. The cross section is always a two-dimensional shape, and varies quite a bit as the cutting angle varies (as you tilt the cutting plane).
Play with cross-sections yourself with these interactive activities from around the web:
How to calculate the area of a circle, plus simple proof for the formula — video lesson
Math Mammoth Geometry 3 — a self-teaching worktext with explanations & exercises (grade 7)
Back to the geometry videos index