Slicing a cube
Move the three sliders to cut the cube with a flat knife. The left picture shows the cut. The right picture shows the slice from straight in front, with its number of sides. Can you find a slice with 3 sides, 4 sides, 5 sides and 6 sides?
- 3 sides
- 4 sides
- 5 sides
- 6 sides
Stuck? Show me one (this gives the game away)
What's going on
The flat face you see when you cut straight through a solid is called a cross-section. Cut a cube level and the cross-section is a square. Tilt the knife and the shape changes.
Every side of the slice is where the knife crosses one face of the cube. A flat knife crosses a flat face in one straight line, so each face gives at most one side. A cube has six faces. That is why you can get 3, 4, 5 or 6 sides, and why no slice of a cube has 7 sides.
A triangle comes from slicing off a corner: the knife crosses the three faces that meet there. For a hexagon the knife must cross all six faces at once. Tilt it so it leans the same way to all three directions and push it through the middle of the cube. Get the tilt exactly right and all six sides are equal.
Sheet: Slicing solids. Related demo: Will it fold?