Nets & Shortest Paths

Unfold a solid to understand it

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A net is a flat pattern that folds into a solid: a cube has 11 of them.
• Surface area is the area of the net.
• Unfolding turns shortest paths on a surface into straight lines (√5 across a cube; 40 ft for Dudeney’s spider).
• A sphere can’t be unfolded, but thin pyramids give its area: 4πr².

Steps

1. Fold it up
2. Which one folds?
3. How many nets?
4. Wrapping a box
5. An ant’s shortcut
6. The surface of a sphere
7. The spider and the fly